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A particle starts from rest and accelera...

A particle starts from rest and accelerates constantly with `2m//s^(2)` for 10 s and then retards uniformly with same rate till it comes to rest. Draw the x-t, v-t and a-t graphs.

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The velocity acquired by the particle at t = 10 s is 20 m/s `(v=u+at)`. It takes further 10 s to comes to rest under retardation of `2m//s^(2)`. Distance travelled in the interval 0 to 10 s is 100 m (use `s=ut+(1)/(2)at^(2)`) and the distance travelled in the interval 10 s to 20 s is also 100 m (use `v^(2)=u^(2)+2as`). Let the particle start from x = 0. The final position of particle is x = 200 m.

Fot t = 0 to t = 10 s, motion is uniformly accelerated with positive acceleration `a=+2m//s^(2)`. The x-t graph is a parabola opening upward. For t = 10 s to t = 20 s, motion is uniformly accelerated with negative acceleration `a=-2m//s^(2)`. The x-t graph is a parabola opening downward.
v-t graph

For t = 0 to t = 10 s, v-t graph is a straight line with positive slope and for t = 10 s to t = 20 s, the v-t graph is a straight line with negative slope. The intial and final velocities are zero.
a-t graph

For t = 0 to t = 10 s, a-t graph is a straight line parallel to time axis with `a=+2m//s^(2)` and for t = 10 s to t = 20 s. The a-t graph is straight line parallel to time axis with `a=-2m//s^(2)`.
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