Question

modifying momentum
two cars of identical mass accelerate at the same rate. car a accelerates for 5 s, and car b accelerates for 10 s.
which of the following statements is true?
car a has a greater impulse than car b.
car b has a greater impulse than car a.
both cars will have the same impulse.

Explanation:

Step1: Recall Impulse Formula

Impulse \( J = F \Delta t \), and from Newton's second law \( F = ma \). Since mass \( m \) and acceleration \( a \) are equal for both cars, the force \( F \) is the same (\( F_A = F_B = ma \)).

Step2: Compare Impulses

For Car A: \( J_A = F \times 5 \)
For Car B: \( J_B = F \times 10 \)
Since \( F \) is positive, \( 10F > 5F \), so \( J_B > J_A \).

Answer:

Car B has a greater impulse than car A.