A 1000 kg car in neutral gear slow from 15 m/s to a stop in 5.0 s due to the force of friction. A. What was the acceleration of the car. B. What was the car’s initial momentum? C. What was its final momentum? D. What was the change in momentum of the car? E. What was the impulse acting on the car? F. How much force stopped the car? G. What distance did the car travel in coming to a stop? H. What was the average velocity of the car as it came to a stop?
To determine the answers to the given questions, we need to use some basic concepts related to Newtonian mechanics. Let's go through each question one by one.
A. What was the acceleration of the car?
To find the acceleration of the car, we can use the formula:
acceleration = change in velocity / time
In this case, the change in velocity is from 15 m/s to 0 m/s, and the time is 5.0 seconds. Therefore,
acceleration = (0 - 15) m/s / 5.0 s
acceleration = -3 m/s²
The negative sign indicates that the car is decelerating or slowing down.
B. What was the car's initial momentum?
The formula to calculate momentum is:
momentum = mass × velocity
The car has a mass of 1000 kg, and the initial velocity is 15 m/s. Therefore,
initial momentum = 1000 kg × 15 m/s
initial momentum = 15000 kg·m/s
C. What was its final momentum?
The final momentum is calculated using the same formula as the initial momentum, but with the final velocity, which is 0 m/s in this case:
final momentum = 1000 kg × 0 m/s
final momentum = 0 kg·m/s
D. What was the change in momentum of the car?
The change in momentum is given by the formula:
change in momentum = final momentum - initial momentum
In this case, the initial momentum was 15000 kg·m/s, and the final momentum was 0 kg·m/s. Therefore,
change in momentum = 0 kg·m/s - 15000 kg·m/s
change in momentum = -15000 kg·m/s
The negative sign indicates that the momentum has decreased.
E. What was the impulse acting on the car?
Impulse is defined as the change in momentum and can be calculated using the formula:
impulse = force × time
Since we know the change in momentum is -15000 kg·m/s and the time is 5.0 seconds, we can rearrange the formula:
force = change in momentum / time
Therefore,
impulse = (-15000 kg·m/s) / 5.0 s
impulse = -3000 N·s (Newton-seconds)
The negative sign indicates that the impulse is in the opposite direction of the car's initial motion.
F. How much force stopped the car?
To find the force that stops the car, we can use the formula:
force = mass × acceleration
The mass of the car is 1000 kg, and the acceleration is -3 m/s². Therefore,
force = 1000 kg × (-3 m/s²)
force = -3000 N (Newton)
The negative sign indicates that the force is acting in the opposite direction of the car's initial motion.
G. What distance did the car travel in coming to a stop?
To find the distance traveled by the car, we can use the formula of motion under constant acceleration:
distance = (initial velocity × time) + (0.5 × acceleration × time²)
In this case, the initial velocity is 15 m/s, the time is 5.0 seconds, and the acceleration is -3 m/s². Therefore,
distance = (15 m/s × 5.0 s) + (0.5 × (-3 m/s²) × (5.0 s)²
distance = 75 m + (-37.5 m)
distance = 37.5 m
The negative sign in the second term shows that the distance is opposite to the initial direction of motion.
H. What was the average velocity of the car as it came to a stop?
The average velocity can be calculated using the formula:
average velocity = (final velocity + initial velocity) / 2
In this case, the final velocity is 0 m/s and the initial velocity is 15 m/s. Therefore,
average velocity = (0 m/s + 15 m/s) / 2
average velocity = 7.5 m/s
Please note that in this case, the average velocity is half the initial velocity because the car is slowing down uniformly.
Surely you know how to compute acceleration given the speed change and time interval. You should also know how to calculate momentum by now.
If you are not going to make an effort, neither am I.