Final answer:
The force acting on the bowling ball as it decelerates is calculated using the formula F = m * a. The correct answer is D) 175 N, reflecting the magnitude of the force required to cause the given change in velocity over the specified time.
Step-by-step explanation:
To calculate the force acting on the 7.00 kg bowling ball as it slows down, we can use Newton's second law of motion which states that force equals mass times acceleration (F = m * a). First, we need to determine the acceleration of the ball by using the formula for acceleration (a = Δv / Δt), where Δv is the change in velocity and Δt is the change in time.
The change in velocity (Δv) is the final velocity minus the initial velocity, which is 7.0 m/s - 8.0 m/s = -1.0 m/s. The negative sign indicates that the ball is decelerating. The time interval (Δt) is 0.040 seconds. So the acceleration is a = Δv / Δt = (-1.0 m/s) / 0.040 s = -25.0 m/s². Now, we can calculate the force by multiplying the mass of the ball by the acceleration: F = m * a = 7.00 kg * (-25.0 m/s²) = -175 N. The negative sign indicates that the force is acting in the opposite direction of the ball's initial motion. Among the options provided, option D) 175 N is the correct answer but without the negative sign since options are given in magnitude form.