First slide

Instantaneous acceleration

Question

A particle starts from rest at the origin and continues to move along positive x-axis with acceleration $2 m / s^{2}$ . After some time it starts moving with constant retardation $3 m / s^{2}$ and finally stops at a point on x-axis. If total time of journey of the particle is 10 sec, find the time during which the particle is accelerated.

Moderate

Solution

$V_{\max} = 0 + 2 t_{1}; also 0 = V_{\max} - 3 t_{2}$
$∴ 2 t_{1} = 3 t_{2} ...... (1)$ and $t_{1} + t_{2} = 10..... (2),$ solving, $t_{1} = 6 \sec$

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