Question

A car and a truck are initially moving in the same direction at 20 m/s with the truck 38m ahead.the car accelerate at a constant 2m/s^2 passes the truck and return to the right lane when it is 11m ahead of the truck.how far has the truck moved during this time?

Answer 1

$$d=vt$$

$$(v+at)^2-v^2=2a(d+s_1+s_2)\\a^2t^2+2vat=2a(d+s_1+s_2)\\a^2\frac{d^2}{v^2}+2va\frac{d}{v}=2a(d+s_1+s_2)\\(2)^2\frac{d^2}{20^2}+2(20)(2)\frac{d}{20}=2(2)(d+11+38)$$

$$d=140\ m$$