Velocity Time Graphs - Definition, Example, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 05:00 PM IST

Here, in this article, we will learn about the velocity time graph/vt graph, vt meaning, velocity time, what is velocity time graph, when the acceleration of a particle is increasing linearly, how to draw velocity time graph, what velocity time graph gives, velocity time graph examples, velocity time relation, velocity vs time graph/velocity versus time graph, constant velocity graph, study the velocity time graph and calculate acceleration, what we studied about velocity time graph class 9, the velocity time graph of a particle, velocity graph, velocity time graph acceleration, how to find acceleration in velocity time graph, zero acceleration graph, the velocity displacement graph of a particle, what does velocity time graph represent etc.

Velocity Time Graphs - Definition, Example, FAQs

What is the Velocity time graph?

A velocity-time graph represents the different velocities of a moving object at different times. We can say that when an object moves with a speed in a particular direction, it is the velocity of that object. Velocity is a vector quantity as it has both direction and magnitude. The velocity-time graph gives the acceleration of an object. We know that acceleration is the rate of change of velocity. The vertical axis of the velocity-time graph is taken as the velocity of the object and horizontal axis as the time elapsed.

On the velocity- time graph, we get different types of acceleration. An object may have a constant velocity, increasing velocity, or decreasing velocity and it can easily be determined whether the object is accelerating, decelerating, or not accelerating at all.

If an object moves with a constant velocity, then we obtain a straight horizontal line on the graph. It means that there is no change in the velocity and as a result, we get no acceleration or zero acceleration.

If an object moves with an increasing velocity or constant acceleration, then we get a straight sloped line on the graph. Here, in this case the acceleration of a particle is increasing linearly.

If an object moves with an increasing acceleration, then we get curved lines.

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Let us study these cases one by one.

Case I:- Constant velocity graph or No Acceleration graph

If the object moves with constant velocity, it means that the initial and final velocity of the object remains the same. The slope obtained in this case will be constant. It leads us to conclude that there is no increase or no decrease in the acceleration of the object and the object will have zero acceleration in this case.

The following VT graph shows zero acceleration.

Constant velocity

Case II:- Increasing Velocity or Constant Acceleration

If the velocity of an object increases throughout its motion, then the final velocity becomes more than the initial velocity. The initial velocity, in this case, can be zero, as the object is constantly increasing its speed. The slope of the velocity-time graph obtained in this case will increase. It leads us to conclude that the body is in constant acceleration.

The following VT graph shows constant acceleration.

constant acceleration

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Case III:- Increasing rate of change of velocity or Increasing acceleration

If the rate of change of velocity increases throughout the motion, then the final velocity will be much more than the initial velocity. The initial velocity in this case can be zero as the acceleration of the object is increasing every second at some rate. The slope of the velocity-time graph in this case will lead us to conclude that the graph will form a curve. Hence, the curve in this slope has increasing/decreasing acceleration.

The following VT graph shows increasing acceleration.

increasing acceleration

We can obtain a decreasing velocity-time graph similar to the increasing velocity-time graph. In this case the slope will decrease as the velocity is decreasing. Here, in this case we will get a negative slope and the acceleration will be decreasing.

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Velocity time graph questions for class 9

Q.1 A particle starts from rest and moves with a uniform acceleration of 5m/s2 for 10s and then it moves with a constant velocity for 4s. Later it slows down and comes to rest in 5s. Draw the velocity graph for the motion of the body and answer the following questions:
a. What is the maximum velocity attained by the body?
b. What is the distance travelled during this period of acceleration?
c. What is distance travelled when the body is moving with constant velocity?
d. What is the retardation of the body while slowing down?
e. What is the distance travelled by retarding?
f. What is the total distance travelled?

Solution)

velocity graph for the motion of the body

(a) Maximum velocity will be reached when acceleration is stopped at the end of the first 10 sec and is shown in graph

V = 50 m/s
(b) Distance is given by the area of the graph enclosed till 10 sec

s = (1/2) X 50 X 10 = 250 m

= 4 X 50 = 200m

(d) Retardation is given by the slope of the curve from B to C

A = (0-50)/5 = - 10 m/s²

(e) Distance = (1/2) X 50 X 5 =125m

(f) Total distance is given by the total area of the graph = 250 + 200 + 125 = 575 m

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Frequently Asked Questions (FAQs)

1. What is the velocity time graph?

A velocity-time graph represents the different velocities of a moving object at different times.

2. What does the velocity time graph represent?

The velocity time graph represents acceleration as we know that the rate of change of velocity gives us acceleration.

3. When is acceleration constant?

When the velocity is constantly increasing, we get constant acceleration in that case.

4. How do you interpret the slope of a velocity-time graph?

The slope of a velocity-time graph represents acceleration. A positive slope indicates positive acceleration (speeding up), a negative slope indicates negative acceleration (slowing down), and a horizontal line (zero slope) indicates constant velocity (no acceleration).

5. What does the area under a velocity-time graph represent?

The area under a velocity-time graph represents the displacement of the object. This is because displacement is the product of velocity and time, which corresponds to the area under the curve on a velocity-time graph.

6. Can velocity be negative on a velocity-time graph?

Yes, velocity can be negative on a velocity-time graph. A negative velocity indicates that the object is moving in the opposite direction to the one defined as positive. For example, if moving right is positive, then a negative velocity means the object is moving left.

7. How do you determine if an object is accelerating from a velocity-time graph?

An object is accelerating if the velocity-time graph is not a horizontal line. Any change in the graph's slope (either increasing or decreasing) indicates acceleration. A curved line also represents acceleration, as the velocity is continuously changing.

8. What does a horizontal line on a velocity-time graph mean?

A horizontal line on a velocity-time graph indicates that the object is moving at a constant velocity. This means the speed and direction of the object remain unchanged over that period of time, and there is no acceleration.

9. What is a velocity-time graph?

A velocity-time graph is a visual representation that shows how an object's velocity changes over time. The vertical axis represents velocity, while the horizontal axis represents time. This graph helps us understand an object's motion, including whether it's speeding up, slowing down, or moving at a constant speed.

10. How can you tell if an object is at rest from a velocity-time graph?

An object is at rest when its velocity is zero. On a velocity-time graph, this would be represented by a horizontal line along the time axis (where velocity = 0). If this line extends for a period of time, it means the object remains at rest for that duration.

11. What's the difference between speed and velocity on a velocity-time graph?

While both speed and velocity are related to how fast an object is moving, velocity includes direction. On a velocity-time graph, the magnitude of velocity represents speed, while the sign (positive or negative) indicates direction. Speed is always positive, but velocity can be positive, negative, or zero.

12. What does a velocity-time graph look like for an object in free fall?

For an object in free fall (ignoring air resistance), the velocity-time graph would be a straight line with a positive slope. The slope of this line represents the acceleration due to gravity (approximately 9.8 m/s² on Earth). The line starts at zero (or the initial velocity) and continues to increase linearly with time.

13. What does the steepness of a velocity-time graph tell you?

The steepness of a velocity-time graph indicates the magnitude of acceleration. A steeper slope means a greater acceleration (positive or negative), while a less steep slope indicates a smaller acceleration. A horizontal line (no steepness) means no acceleration.

14. What does a sinusoidal curve on a velocity-time graph represent?

A sinusoidal curve on a velocity-time graph represents periodic motion, such as that of a simple harmonic oscillator (like a mass on a spring). It indicates that the velocity is continuously changing, alternating between positive and negative values in a regular pattern.

15. How can you tell if two objects will collide from their velocity-time graphs?

You cannot definitively tell if two objects will collide just from their velocity-time graphs. While these graphs show how the velocities change over time, they don't provide information about the objects' positions. To determine if a collision will occur, you'd need additional information about the objects' initial positions and their paths.

16. How do you represent the motion of a pendulum on a velocity-time graph?

The motion of a pendulum on a velocity-time graph would be represented by a sinusoidal curve. The velocity oscillates between positive and negative values as the pendulum swings back and forth. The amplitude of the curve represents the maximum speed of the pendulum, which occurs at the bottom of its swing.

17. How do you calculate average velocity from a velocity-time graph?

To calculate average velocity from a velocity-time graph, you need to find the total displacement (area under the curve) and divide it by the total time. Graphically, this is equivalent to drawing a straight line from the start point to the end point of the curve and finding its slope.

18. How can you determine the direction of motion from a velocity-time graph?

The direction of motion can be determined from the sign of the velocity on the graph. Positive velocity values indicate motion in the direction defined as positive, while negative values indicate motion in the opposite direction. A change from positive to negative (or vice versa) indicates a change in direction.

19. How do you represent deceleration on a velocity-time graph?

Deceleration is represented on a velocity-time graph by a line with a negative slope. This means the velocity is decreasing over time. If the object is moving in the positive direction, the line will slope downwards towards the time axis. If moving in the negative direction, the line will slope upwards towards the time axis.

20. Can a velocity-time graph have vertical lines?

No, a velocity-time graph cannot have vertical lines. A vertical line would imply an instantaneous change in velocity, which is physically impossible as it would require infinite acceleration. In reality, all changes in velocity take some amount of time, no matter how small.

21. How do you represent a sudden stop on a velocity-time graph?

A sudden stop is represented on a velocity-time graph by a steep (but not vertical) line dropping to zero velocity. The steepness of this line represents the rapid deceleration. After reaching zero, the line would continue horizontally along the time axis, indicating the object remains at rest.

22. What does a parabolic curve on a velocity-time graph indicate?

A parabolic curve on a velocity-time graph indicates that the object is experiencing constant acceleration or deceleration. If the parabola opens upward, it represents constant positive acceleration. If it opens downward, it represents constant negative acceleration (deceleration).

23. How can you tell if an object has returned to its starting point from a velocity-time graph?

You cannot directly tell if an object has returned to its starting point from a velocity-time graph alone. However, if the area above the time axis equals the area below it, the net displacement is zero, which could mean the object has returned to its starting point. To be certain, you'd need additional information or a position-time graph.

24. What's the relationship between velocity-time graphs and position-time graphs?

The velocity-time graph is the derivative of the position-time graph, and conversely, the position-time graph is the integral of the velocity-time graph. In other words, the slope of a position-time graph at any point gives the velocity at that time, while the area under a velocity-time graph gives the change in position.

25. How do you represent an object moving with constant speed but changing direction on a velocity-time graph?

An object moving with constant speed but changing direction would be represented by a sudden jump from a positive to a negative velocity (or vice versa) of the same magnitude. This would appear as a vertical line on the graph, but remember that in reality, this change would happen very quickly but not instantaneously.

26. How can you determine the total distance traveled from a velocity-time graph?

To determine the total distance traveled, you need to calculate the area under the velocity-time graph, but taking the absolute value of velocity. This means you sum up all areas, regardless of whether the velocity is positive or negative. This differs from displacement, which considers direction.

27. What does a velocity-time graph look like for an object thrown vertically upward and then falling back down?

For an object thrown vertically upward and falling back down, the velocity-time graph would start with a positive velocity (upward motion), decrease linearly due to gravity until it reaches zero (at the highest point), and then continue to decrease into negative values (downward motion). The graph would be a straight line with a negative slope, passing through zero.

28. How do you represent acceleration on a velocity-time graph when it's not constant?

When acceleration is not constant, the velocity-time graph will not be a straight line. Instead, it will be a curve. The changing slope of this curve at different points represents the varying acceleration. A steeper section of the curve indicates higher acceleration, while a flatter section indicates lower acceleration.

29. Can a velocity-time graph cross the time axis? What does this mean?

Yes, a velocity-time graph can cross the time axis. This crossing point represents the moment when the object's velocity is zero. It often indicates that the object has changed direction. For example, when throwing a ball upwards, it will momentarily stop at its highest point before falling back down.

30. How do you represent an object moving in circles on a velocity-time graph?

Representing circular motion on a velocity-time graph depends on how you define velocity. If you're considering the magnitude of velocity (speed), it would be a horizontal line if the speed is constant. If you're considering velocity in one dimension (like x or y), it would be a sinusoidal curve, as the component of velocity in that direction changes periodically.

31. What does the intersection of two lines on a velocity-time graph represent?

The intersection of two lines on a velocity-time graph represents a point where two objects have the same velocity at the same time. This could mean they are at the same position if they're moving along the same path, but not necessarily if they're on different paths.

32. What does a velocity-time graph look like for an object in simple harmonic motion?

For an object in simple harmonic motion, like a mass on a spring, the velocity-time graph would be a cosine or sine curve. The velocity oscillates between positive and negative values, representing back-and-forth motion. The amplitude of this curve represents the maximum speed of the object.

33. How do you represent a car's journey with stops at traffic lights on a velocity-time graph?

A car's journey with stops at traffic lights would be represented by a series of triangular or trapezoidal shapes on a velocity-time graph. Each shape would represent a period of acceleration (increasing velocity), constant speed (horizontal line), and deceleration (decreasing velocity). The stops would be shown as horizontal lines along the time axis where velocity is zero.

34. What does a velocity-time graph look like for an object moving with constant acceleration?

For an object moving with constant acceleration, the velocity-time graph would be a straight line. If the acceleration is positive, the line would slope upward (increasing velocity over time). If the acceleration is negative, the line would slope downward (decreasing velocity over time). The slope of this line represents the constant acceleration.

35. How can you determine the instantaneous velocity at any point from a velocity-time graph?

The instantaneous velocity at any point on a velocity-time graph is simply the y-coordinate of that point. You can read this directly from the graph by drawing a horizontal line from the point of interest to the velocity axis.

36. What does a velocity-time graph look like for an object bouncing on a surface?

For an object bouncing on a surface, the velocity-time graph would show a repeating pattern of straight lines. Each bounce would be represented by a rapid change from downward velocity (negative) to upward velocity (positive). Between bounces, the lines would slope downward due to gravitational acceleration.

37. What does the area between the velocity-time graph and the time axis represent?

The area between the velocity-time graph and the time axis represents the displacement of the object. Areas above the time axis (positive velocity) contribute positive displacement, while areas below the axis (negative velocity) contribute negative displacement. The net area gives the overall displacement.

38. How can you tell if an object is speeding up or slowing down from a velocity-time graph?

To determine if an object is speeding up or slowing down, look at both the velocity and the slope of the graph:

39. What does a velocity-time graph look like for an object in projectile motion?

For an object in projectile motion, you would typically have two separate velocity-time graphs - one for horizontal motion and one for vertical motion. The horizontal velocity graph would be a horizontal line (constant velocity). The vertical velocity graph would be a straight line with a negative slope due to gravitational acceleration, starting from the initial vertical velocity.

40. How do you represent the motion of an elevator on a velocity-time graph?

The motion of an elevator on a velocity-time graph would typically show several phases:

41. What does a velocity-time graph look like for a car accelerating to highway speed, then maintaining that speed?

This velocity-time graph would have two distinct sections:

42. How can you determine the average acceleration from a velocity-time graph?

The average acceleration can be determined from a velocity-time graph by calculating the slope of the line connecting the initial and final points of the interval in question. Mathematically, this is (final velocity - initial velocity) / (final time - initial time). Graphically, it's the slope of the straight line from the start point to the end point of the interval.

43. What does a velocity-time graph look like for an object experiencing air resistance while falling?

For an object falling with air resistance, the velocity-time graph would start with a steep negative slope (acceleration due to gravity), but this slope would gradually decrease as the air resistance increases. Eventually, the graph would approach a horizontal line, representing terminal velocity, where the force of air resistance equals the force of gravity.

44. How do you represent the motion of a yo-yo on a velocity-time graph?

A yo-yo's motion on a velocity-time graph would show a repeating pattern:

45. What does a velocity-time graph look like for a ball rolling down a hill and then up another hill?

This velocity-time graph would have three main sections:

46. How can you tell the difference between uniform motion and uniformly accelerated motion on a velocity-time graph?

Uniform motion (constant velocity) is represented by a horizontal line on a velocity-time graph, as the velocity doesn't change over time. Uniformly accelerated motion is represented by a straight line with a non-zero slope, as the velocity is changing at a constant rate over time.

47. What does a velocity-time graph look like for a person walking, then running, then walking again?

This velocity-time graph would have three distinct sections:

48. How do you represent the motion of a car braking to a stop on a velocity-time graph?

A car braking to a stop would be represented by a line with a negative slope on a velocity-time graph. The line would start at the car's initial velocity and decrease to zero. The slope of this line represents the deceleration rate. If the braking is constant, the line will be straight. If the braking force varies, the line might be curved, with the slope becoming steeper as the car slows down.