The acceleration (a) of a particle moving in a straight line varies with its displacement (s) as `a=2s+1`. The velocity of the particle is zero at zero displacement. Find the corresponding velocity-displacement equation.

Explanation

For `0 le t le 5 v prop t rArr s prop t^(2)` and `a_(1)=` constant `10/5=2 m//s^(2)`
for whole interval `s_(1)=` Area under the curve `=1/2 xx5xx10=25 m`
For `5 le t le 10, v=10 ms^(-1)rArr a=0`
for whole interval `s_(2)=` area under the curve `=5xx10=50 m`
For `10 le t le 12` v linearly decreases decreases with time `rArr a_(3)=-10/2=-5 ms^(-2)`
for whole interval `s_(3)=` Area under the curve `=1/2xx2xx10=10 m`