A car starts from rest and accelerates uniformly at 3.0 m/s² toward the north.A second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s² toward the north.How long after the second car starts does it overtake the first car? A)12 s B)19 s C)21 s D)24 s

Question

Quizplus · Accepted Answer

Let's assume that the distance covered by the first car at the time when the second car starts is "d" meters. 
Then, the position of the first car after time "t" seconds can be given by: 
distance_1 = (1/2)at^2, where a = 3.0 m/s^2 and distance_1 = d + (1/2)at^2

Similarly, the position of the second car after time "t" seconds can be given by: 
distance_2 = (1/2)at^2, where a = 5.0 m/s^2 and distance_2 = (1/2)a(t-6)^2

Now, we need to find the value of "t" when distance_1 = distance_2: 
d + (1/2)at^2 = (1/2)a(t-6)^2 
Solving this equation gives t = 21 seconds. Hence, the second car overtakes the first car 21 seconds after it starts.

A Car Starts from Rest and Accelerates Uniformly at 3