Question

A car company wants to ensure its newest model can stop in 8 sec when traveling at 70 mph. If we assume constant deceleration, find the value of deceleration (in ft/sec) that accomplishes this. (Round your answer to two decimal places.) ____ ft/sec²

Answer 1

To find the deceleration of the car, use the equation of motion and solve for deceleration. The deceleration is -8.75 ft/sec².

Step-by-step explanation:

To find the value of deceleration that accomplishes a car stopping in 8 seconds when traveling at 70 mph, we can use the equation of motion:

v = u + at

where v is the final velocity, u is the initial velocity, a is the deceleration, and t is the time.

Given that the final velocity is 0 (since the car stops), the initial velocity is 70 mph (which we need to convert to ft/sec), and the time is 8 seconds, we can rearrange the equation to solve for deceleration:

a = (v - u) / t

Plugging in the values, we get:

a = (0 - 70 ft/sec) / 8 sec

a = -8.75 ft/sec²

Therefore, the value of deceleration that accomplishes the car stopping in 8 seconds when traveling at 70 mph is -8.75 ft/sec².