Question

A car starts from rest and reaches a speed of 45km/hr in 20s. it travels at this speed for ½ a kilometre and then comes to rest uniformly in 30 s Find;

a)Acceleration

b)total distance traveles

Answer 1

Given:

$v_0=0, \quad v_1=45\:\rm km/hr=12.5\: m/s$

$t_1=20\:\rm s$

$d_2=500\:\rm m$

$t_3=30\:\rm s$

$v_4=0$

(a)

$$a_1=\frac{\Delta v}{\Delta t}=\frac{v_1-v_0}{t_1}=\frac{12.5-0}{20}=0.625\:\rm m/s^2$$

$$a_3=\frac{\Delta v}{\Delta t}=\frac{v_4-v_1}{t_3}=\frac{0-12.5}{30}=-0.417\:\rm m/s^2$$

(b)

$$d=d_1+d_2+d_3\\ =\frac{v_1+v_0}{2}t_1+d_2+\frac{v_4+v_1}{2}t_3\\ =\frac{12.5+0}{2}*20+500+\frac{0+12.5}{2}30=813\:\rm m$$