Answer to Question #236399 in Mechanics | Relativity for Jick

Question

A truck is stopped at a stoplight. When the light turns green, it accelerates at 2.5 m/s2. At the same instant, a car passes the truck going 15 m/s. Where and when does the truck catch up with the car?

Answer 1

Truck

$u_t=0 \\ v_t^2 = 2a_ts_t$

Car

$u_c= 15 \;m/s \\ S= u_ct_c \\ S = 15t_c$

Time taken by truck = Time taken by car

$t_t =t_c \\ v_t = at_t \\ S= \frac{1}{2}at^2 = \frac{1}{2}(2.5)t^2 \\ 15t_k = \frac{1}{2}(2.5)t^2 \\ \frac{30}{2.5} = t_c \\ t_c=12\;s \\ S= 15 \times 12 = 180 \;m$

At time 12 sec and distance 180 m both vehicles will meet.