Answer to Question #225031 in Classical Mechanics for Ace

Question

5.At the instant, traffic light turns green, an automobile that has been waiting at an intersection of roads accelerate with 5m/s. At the same instant a truck travelling with a constant velocity of 20m/s overtake and passes the automobile.
a.How far beyond it's starting point will the automobile overtake the truck.
b.How fast will it be travelling?

Answer 1

$\text{for automobile:}$

$v_0 =0;a= 5\frac{m}{s^2}$

$s_{aut}(t) = v_0t+\frac{at^2}{2}=\frac{5t^2}{2}$

$v_{aut}(t)= v_0+at = 5t$

$\text{for truck:}$

$v_{tr}= 20\frac{m}{s}$

$s_{tr}(t) = v_{tr}t= 20 t$

$s_{aut} = s_{tr}$

$\frac{5t^2}{2}= 20t$

$t_1= 0 \text{ this is the beginning of the movement}$

$t_2 = 8s$

$s_{tr}(t_2) = 20 *t_2= 160m$

$v_{aut}(t_2)=5t_2= 40\frac{m}{s}$

$\text{Answer: }a.$160 m b.$40\frac{m}{s}$