Question

In a car race car A takes time to get less then car B, reaches the finishing point with a velocity v more than car B. Assuming cars start from rest, travel with constant accelerations a1 and a2 respectively. Show that v/t=✓a1a2

Answer 1

For car A:

t_a=t'-t

v_a=u+v

For car B:

t_b=t'

v_b=u

s=(1/2) a_1 (t^'-t)^2=(1/2) a_2 (t^' )^2

Thus,

(1-t/t^' )=(a_2/a_1 )^(1/2)

(u+v)^2=2a_1 s

(u)^2=2a_2 s

So,

(1+v/u)=(a_1/a_2 )^(1/2)

But

u=a_2 t'

So

v/t=(a_1 a_2 )^(1/2)