Question

A truck moves from rest with a uniform acceleration of 2m/s^2 for the first 10sec, it then accelerates at a uniform rate of 1m/s^2 for another 15sec, it continues at a constant speed for 70sec an finally come to rest in 20sec by uniform retardation.

Answer 1

Given:

$a_1=2\:\rm m/s^2$

$a_2=1\:\rm m/s^2$

$t_1=10\:\rm s$

$t_2=15\:\rm s$

$t_3=70\:\rm s$

$t_4=20\:\rm s$

The total distance

$$d=d_1+d_2+d_3+d_4$$

1.

$$d_1=\frac{a_1t_1^2}{2}=\frac{2*10^2}{2}=100\:\rm m$$

2.

$$v_2=a_1t_1=2*10=20\:\rm m/s$$

$$d_2=v_2t_2+\frac{a_2t_2^2}{2}=20*15+\frac{1*15^2}{2}=412.5\:\rm m$$

3.

$$v_3=v_2+a_2t_2=20+1*15=35\:\rm m/s$$

$$d_3=v_3t_3=35*70=2450\:\rm m$$

4.

$$d_4=\frac{v_3+0}{2}t_4=\frac{35+0}{2}*20=350\:\rm m$$

Finally,

$$d=100+412.5+35+2450+350=3312.5\:\rm m$$