Question

An electric train moves from rest with a uniform acceleration of 1.5 for the first 10s and continues accelerating at 0.5 for a further 20s. It continues at a constant speed for 90s and finally takes 30s to decelerate uniformly to rest.

Using the equations of motion calculate the total distance travelled

Answer 1

$a_1=1.5,$ $t_1=10,$ $a_2=0.5,$ $t_2=20,$ $t_3=90,$ $t_4=30.$

$s_1=\frac{a_1 t_1^2}{2}=75~m.$

$v_1=a_1t_1=15~\frac ms,$

$s_2=v_1t_2+\frac{a_2t_2^2}{2}=400~m.$

$v_2=v_1+a_2t_2=25~\frac ms,$

$s_3=v_2t_3=225~m.$

$0=v_2-a_3t_4,$

$a_3=\frac{v_2}{t_4},$

$s_4=v_2t_4-\frac{a_3t_4^2}{2}=\frac{v_2t_4}{2}=375~m.$

$s=s_1+s_2+s_3+s_4=1075~m.$