Question

two cars accelerate at the same rate. car a accelerates for 3 s, and car b accelerates for 7 s. which of the following is true about the impulse of the cars? the impulse of car b is less than the impulse of car a. both cars will have the same impulse. the impulse of car a is less than the impulse of car b.

Explanation:

Step1: Recall the impulse formula

Impulse \(J = F\times t\). According to Newton's second law \(F = ma\). Since the two cars have the same acceleration \(a\) (assuming their masses \(m\) are the same, as the problem only mentions acceleration rate and time of acceleration, and in the context of comparing impulse when acceleration rate is same, mass is usually considered same for a fair comparison of the effect of time on impulse).

Step2: Compare the impulse of two cars

For car A, \(J_A=F\times t_A = ma\times t_A\). For car B, \(J_B = ma\times t_B\). Given \(t_A = 3s\) and \(t_B=7s\), and \(m\) and \(a\) are the same for both cars. Since \(t_A

Answer:

The impulse of car A is less than the impulse of car B.