First slide

The 3 equation for uniform acc

Question

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

Moderate

A

33%
B

40%
C

66%
D

77%

Solution

We know that, $s_{n t h} = u + \frac{1}{2} a (2 n - 1)$
$s_{3 r d} = 0 + \frac{1}{2} a (2 \times 3 - 1) = \frac{5}{2} a$ (For n = 3s)
$s_{rrd} = 0 + \frac{1}{2} a (2 \times 4 - 1) = \frac{7}{2} a$ (For n = 4s)
So, the percentage increase $= \frac{s_{4 th} - s_{3 rd}}{s_{3 rd}} \times 100$
$= \frac{\frac{7}{2} a - \frac{5}{2} a}{\frac{5}{2} a} \times 100 = \frac{\frac{2 a}{2}}{\frac{5}{2} a} \times 100 = 2 \times 20 = 40 %$

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