First slide

Rectilinear Motion

Question

A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in the displacement during the 4^th sec compared to that in the 3^rd sec is…

Easy

A

30%
B

70%
C

40%
D

60%

Solution

Given $u = 0 n_{1} = 3 n_{2} = 4$
From the equation $s_{n} = u + a (n - \frac{1}{2})$
$\begin{array}{l} s_{3} = a (3 - \frac{1}{2}) = \frac{5 a}{2} \\ s_{4} = a (4 - \frac{1}{2}) = \frac{7 a}{2} \end{array}$
The percentage increase in the 4^th sec s
$\begin{array}{l} = \frac{s_{4} - s_{3}}{s_{3}} \times 100 % \\ = (\frac{\frac{7 a}{2} - \frac{5 a}{2}}{(\frac{5 a}{2})}) \times 100 \\ = \frac{2}{5} \times 100 = 40 % . \end{array}$

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