Driving home from school one day, you spot a ball rolling out into the street (see the figure ). You brake for 1.00 , slowing your 970- car from 16.0 to 9.50 .
What was the magnitude of the average force exerted on your car during braking?
How far did you travel while braking?
To determine the magnitude of the average force exerted on your car during braking, you can use the equation:
Force = (mass) x (acceleration).
First, let's find the mass of your car. The problem states that your car is 970 kg.
Next, we need to find the acceleration. We can use the following formula:
acceleration = (final velocity - initial velocity) / time.
The problem states that your car slowed down from 16.0 m/s to 9.50 m/s over a time of 1.00 s.
Using these values, we can calculate the acceleration:
acceleration = (9.50 m/s - 16.0 m/s) / 1.00 s = -6.50 m/s².
Note that the negative sign indicates deceleration (slowing down).
Now we can calculate the magnitude of the average force:
Force = (mass) x (acceleration) = 970 kg x -6.50 m/s² = -6310 N.
The magnitude of the average force exerted on your car during braking is 6310 N.
To find the distance traveled while braking, we can use the following equation:
distance = initial velocity x time + (1/2) x acceleration x time².
Plugging in the given values:
distance = 16.0 m/s x 1.00 s + (1/2) x (-6.50 m/s²) x (1.00 s)².
Simplifying:
distance = 16.0 m + (-3.25 m) = 12.75 m.
Therefore, while braking, you traveled a distance of 12.75 meters.