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A body initially at rest is moving with uniform acceleration 'a' m/s2 .it's velocity after 'n' second is 'v' the displacement of the body in last 2s is .?


Chandrakanth 1st Aug, 2020
Answer (1)
Prabhav Sharma 1st Aug, 2020

Hello Chandrakanth,

We know that distance travelled in t seconds is given by the relation:

S = u * t + ½ * a * t^2

Where u = initial velocity in m/s

A = acceleration in m/s^2

T = time in s

Here, u = 0, a = a, t = n (given)

Therefore, distance travelled after n seconds is:

Sn = 0 * n + ½ * a * n^2 = ½ * a * n^2

also, distance travelled in n-2 seconds will be:

S(n-2) = 0 * (n – 2) + ½ * a * (n-2) = ½ * a * (n–2)^2

Therefore, distance travelled in last 2 seconds will be:

Sn – S(n-2) = ½ * a * n^2 - ½ * a * (n–2)^2

Solving the equation, we get,

Sn – S(n-2) = 2a * (n-1) (Answer) (Equation 1)

Also, we know that v = u + at

Substituting the values, we get, v = an

Substituting the value of a in equation 1, we get

Sn – S(n-2) = 2v/n * (n-1) (Answer)

Hope this is clear!




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