The acceleration-time graph of a body is show | vedclass

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Question

(c) From given $a - t$ graph it is clear that acceleration is increasing at constant rate

$	herefore $ $\frac{{da}}{{dt}} = k$ (constant) $&rArr;$

Vedclass · Accepted Answer

Vedclass · Answer

(c) From given $a - t$ graph it is clear that acceleration is increasing at constant rate

$	herefore $ $\frac{{da}}{{dt}} = k$ (constant) $&rArr;$ $a = kt$ (by integration)

$&rArr; \frac{{dv}}{{dt}} = kt$ $&rArr;$ $dv = ktdt$

$&rArr; \int_{}^{} {dv} = k\int_{}^{} {tdt} $ $&rArr;$ $v = \frac{{k{t^2}}}{2}$

i.e. $v$ is dependent on time parabolically and parabola is symmetric about v-axis.
and suddenly acceleration becomes zero. i.e. velocity becomes constant.

Hence $(c)$ is most probable graph.

The acceleration-time graph of a body is shown below The most probable velocity-time graph of the body is

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