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Different question variety formed

Question

A particle starts moving from rest along a straight line with constant acceleration of 2 $m / s^{2}$ . After 4 second it starts moving with constant retardation of 4 $m / s^{2}$ and finally stops. Then total distance covered by the particle is

Moderate

A

16 m
B

36 m
C

24 m
D

32 m

Solution

Maximum velocity of the particle, $V = (0 + 2 \times 4) m / s = 8 m / s$ .
$∴ x_{1} = 0 \times 4 + \frac{1}{2} \times 2 \times {(4)}^{2} m = 16 m$
and $0 = {(8)}^{2} - 2 \times 4 \times x_{2} \Rightarrow x_{2} = \frac{64}{8} m = 8 m$
$∴$ Total distance covered, $x = x_{1} + x_{2} = (16 + 8) m = 24 m$

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