Answer to Question #93130 in Mechanics | Relativity for Cyrelle Laureano Senorin

Question

5.) A car traveling at 15 m/s passes a van that is starting from rest with an acceleration of 3 m/s². (a) How long will it take the van to catch up with the car? (b) How far has the car traveled when the van catches up with it?

Answer 1

The equation of the path traveled by the car

$$S_c=u*t;$$

u=15 m/s;

The equation of the path traveled by the van

$$S_v=\frac{a*t^2}{2};$$

a= 3 m/s^2;

a) When the truck catches up with the car:

$$S_c=S_v; \\u*t=\frac{a*t^2}{2}; \\ t=\frac{2*u}{a} \\t=10s;$$

b)substitute time into the equation Sc:

$$S_c=u*t; \\S_c=150 m$$