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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