First slide

Rectilinear Motion

Question

A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is

Moderate

A

$\frac{v (n + 1)}{n}$
B

$\frac{2 v (n + 1)}{n}$
C

$\frac{2 v (n - 1)}{n}$
D

$\frac{v (n - 1)}{n}$

Solution

$v = 0 + n a \Rightarrow a = \frac{v}{n}$
displacement in last two seconds
$\begin{array}{l} s (n) - s (n - 2) \\ = (0 + \frac{1}{2} a n^{2}) - (0 + \frac{1}{2} a (n - 2)^{2}) \\ = 2 a (n - 1) = 2 v \frac{(n - 1)}{n} \end{array}$

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