The standard brakes on a car cause a negative acceleration of -8 mph/s. If a car is traveling at 50 mph when the driver applies the brakes, how long will it take for the car to stop?

Question

16-04-2024
Mathematics

High School

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The standard brakes on a car cause a negative acceleration of -8 mph/s. If a car is traveling at 50 mph when the driver applies the brakes, how long will it take for the car to stop?

Answer :

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TaylorSmith4590 TaylorSmith4590 · Answer 1 · 2024-11-21T02:47:30-05:00

The car experiencing a negative acceleration of -8 mph/s while traveling at 50 mph will come to a stop after 6.25 seconds. This negative acceleration is in the direction opposite to the car's motion.

Understanding Negative Acceleration in Car Braking

When a car is moving in a negative direction and the brakes are applied, the acceleration of the car is also in the negative direction. This is because acceleration refers to the rate of change of velocity, and when a car is slowing down, its acceleration is opposite to the direction of its velocity.

In the example provided, if a car is traveling at 50 mph and applies brakes that cause a negative acceleration of –8 mph/s, we can calculate the time it takes for the car to stop.

To find the time, we use the formula:

Final velocity (Vf) = Initial velocity (Vi) + (Acceleration (a) * Time (t))
0 mph = 50 mph + (–8 mph/s * t)
Then solve for t: t = (0 mph – 50 mph) / (–8 mph/s).
The time, t, to stop the car is 6.25 seconds.

Therefore, the car will come to a stop after 6.25 seconds when brakes with a negative acceleration of –8 mph/s are applied while the car is moving at 50 mph.