Question

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

Answer 1

The car decelerated for approximately 0.77 hours, or about 46.2 seconds, from a speed of 75 miles per hour to a complete stop with a deceleration rate of -98 miles/hr².

Step-by-step explanation:

To determine how long it took the car to decelerate to a complete stop, we can use the formula for acceleration, which is a = ∆v/∆t, where a is acceleration, ∆v is the change in velocity, and ∆t is the change in time. The change in velocity (∆v) is 75 miles per hour, since the car comes to a stop, and the deceleration given is -98 miles/hr².

Rearranging the formula to solve for ∆t gives us ∆t = ∆v/a. Therefore, plugging in the values, we have ∆t = 75 miles per hour/98 miles/hr²

. The deceleration must be taken as a positive value since it is a magnitude in this context, which results in a time of approximately 0.77 hours, or about 46.2 seconds, to decelerate completely.