A car is traveling at 7.0 m/s when the driver applies the brakes. the car move 1.5m before it comes toa complete stop. if the car had been moving at 14m/s how far would it have continued to move after the brakes were applied? assume the braking force is constant. what is the formula i should use?
6.0m
To solve this problem, you can use the equations of motion and the concept of uniform acceleration. The formula you will need is the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (0 m/s, since the car comes to a complete stop)
- u is the initial velocity (7.0 m/s in the first scenario and 14 m/s in the second scenario)
- a is the acceleration
- s is the distance traveled
In the first scenario:
Given u = 7.0 m/s, v = 0 m/s, and s = 1.5 m, the formula becomes:
0^2 = 7.0^2 + 2a(1.5)
Simplifying the equation gives:
0 = 49 + 3a
Rearranging the equation gives:
3a = -49
Dividing both sides by 3 gives:
a = -49/3 ≈ -16.33 m/s^2
Now, we can use this value of acceleration to find the distance traveled in the second scenario:
Given u = 14 m/s, v = 0 m/s, and a = -16.33 m/s^2, the formula becomes:
0^2 = 14^2 + 2(-16.33)s
Simplifying the equation gives:
0 = 196 - 32.66s
Rearranging the equation gives:
32.66s = 196
Dividing both sides by 32.66 gives:
s ≈ 6 m
Therefore, if the car had been moving at 14 m/s, it would have continued to move approximately 6 meters after the brakes were applied.