Question

car a slows from 60 mph to 10 mph in 5 s. car b slows from 60 mph to 10 mph in 10 s. if both cars have the same mass, what is true of the forces acting on them? the force on car a is greater than the force on car b. the force on car b is greater than the force on car a. the force acting on both cars is the same.

Explanation:

To determine the forces on the cars, we use Newton's second law \( F = ma \), where \( a=\frac{\Delta v}{\Delta t} \). Both cars have the same mass (\( m \)) and the same change in velocity (\( \Delta v = 60 - 10 = 50 \) mph). Car A has a smaller time interval (\( \Delta t_A = 5 \) s) than Car B (\( \Delta t_B = 10 \) s). Since \( a=\frac{\Delta v}{\Delta t} \), a smaller \( \Delta t \) gives a larger acceleration (\( a_A > a_B \)). Then, from \( F = ma \), with the same \( m \), a larger acceleration means a larger force (\( F_A > F_B \)).

Answer:

The force on car A is greater than the force on car B.