Question

A car starts to move at rest. It travels first 3km with a constant accelaration. Then it travels a distance of 7km with the obtained constant velocity. Then it decelerates for 2.5km and comes to rest. The total time taken for the journey is 15 minutes. The car travels along a straight road. Find the accelaration.

Answer 1

$t=\frac{v}{a_1}+\frac{s_2}v+\frac v{a_2},$

$s_1=\frac{v^2}{2a_1},~s_3=\frac{v^2}{a_2},\implies$

$a_1s_1=a_2s_3,\implies$ $a_2=a_1\frac{s_1}{s_3},$

$t=\frac{s_2}v+\frac{v}{a_1}+\frac{vs_3}{a_1s_1}=\frac{s_2}v+\frac{v}{a_1}(1+\frac{s_3}{s_1}),$

$a_1=\frac{v^2}{2s_1},\implies$

$t=\frac{s_2}v+\frac{2s_1}v(1+\frac{s_3}{s_1})=\frac{s_2+2(s_1+s_3)}v,$

$v=\frac{s_2+2(s_1+s_3)}t=20~\frac ms,$

$a_1=\frac{v^2}{2s_1}=0.067~\frac m{s^2},$

$a_2=\frac{v^2}{2s_3}=0.08~\frac m{s^2}.$