Question

a bus moves from rest with a uniform acceleration of 2ms² for the first 10 seconds. it then accelerate at a uniform rate of 1ms² for another 15seconds. it continues at a constant speed for 70seconds and finally came to rest in 20seconds by uniform acceleration. calculate the average retardation as the body is brought to rest

Answer 1

$v_1=a_1t_1=20~\frac ms.$

$s_1=\frac{a_1t_1^2}{2}=100~m.$

$v_2=v_1+a_2t_2=20+15=35~\frac ms.$

$s_2=v_1t_2+\frac{a_2t_2^2}{2}=300+112.5=412.5~m.$

$s_3=v_2t_3=2450~m.$

$a_3=\frac{v_2}{t_4}=1.75~\frac{m}{s^2}.$

$s_4=\frac{a_3t_4^2}{2}=350~m.$

$s=s_1+s_2+s_3+s_4=3312.5~m.$

$t=t_1+t_2+t_3+t_4=115~s.$

$v=\frac st\approx 28.8~\frac ms.$