Question

A car us driving 75 miles per hour down the interstate and sees a wreck in the distance. The car starts slowing down, but takes a while until it completely comes to a stop. If the acceleration was -98miles:hr^2, how long did it take for the car to decelerate?

Answer 1

To calculate the deceleration time for a car going from 75 mph to a complete stop with an acceleration of -98 miles per hour squared, we convert the given units to seconds and use the kinematic equation v = u + at. We find the deceleration time to be approximately 0.765 seconds.

Step-by-step explanation:

To determine how long it took for the car to decelerate to a complete stop from a speed of 75 miles per hour with a deceleration of -98 miles per hour squared, we can use the kinematic equation that relates velocity, acceleration, and time:

v = u + at

Where v is the final velocity (0, since the car stops), u is the initial velocity (75 mph), a is the acceleration (-98 mph²), and t is the time.

Firstly, let's convert the speed to miles per second by dividing by 3600 (the number of seconds in an hour):

75 mph / 3600 = 0.02083 miles per second

Similarly, we convert the acceleration:

-98 mph² / 3600 = -0.02722 miles per second squared

Now we substitute these values into our equation and solve for t:

0 = 0.02083 + (-0.02722)t

t = 0.02083 / 0.02722

t ≈ 0.765 seconds

Thus, the deceleration time for the car is approximately 0.765 seconds.