An 1800 kg car traveling at 35.0 m/s strikes a wall. If the car comes to rest in 0.500 seconds, then the magnitude of the average force of the wall on the car is
Question
An 1800 kg car traveling at 35.0 m/s strikes a wall. If the car comes to rest in 0.500 seconds, then the magnitude of the average force of the wall on the car is
Solution
To solve this problem, we need to use the formula for force, which is mass times acceleration (F = ma).
First, we need to find the acceleration of the car. Acceleration is the change in velocity over time. In this case, the car goes from 35.0 m/s to 0 m/s in 0.500 seconds. So, the change in velocity is -35.0 m/s (final velocity - initial velocity = 0 m/s - 35.0 m/s = -35.0 m/s).
The time it takes for this change to occur is 0.500 seconds. So, the acceleration of the car is -35.0 m/s divided by 0.500 s, which equals -70.0 m/s². The negative sign indicates that this is a deceleration.
Next, we use the formula for force. The mass of the car is 1800 kg and the acceleration is -70.0 m/s². So, the force is 1800 kg times -70.0 m/s², which equals -126,000 N.
The negative sign indicates that the force is in the opposite direction of the motion of the car, which makes sense because the wall is stopping the car.
However, the question asks for the magnitude of the force, which is a positive value. So, the magnitude of the average force of the wall on the car is 126,000 N.
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