Question

spotting a police car, you hit the brakes on your newporsche to reduce your speed from 90 mi/hto60mi/hat a constant rate over a distance of 200 ft.(a) find the acceleration in ft/s2.(b) how long does it take for you to reduce your speed to55 mi/h?(c) at the acceleration obtained in part (a), how longwould it take for you to bring your porsche to a com-plete stop from 90 mi/h?

Answer 1

The acceleration in ft/s² is -1.65 ft/s². It takes 2.48 s to reduce the speed to 55 mi/h, and it takes 1.51 s to bring the car to a complete stop from 90 mi/h.

Step-by-step explanation:

(a) To find the acceleration in ft/s², we need to convert the initial and final speeds from mi/h to ft/s. We can use the formula:

acceleration = (final velocity - initial velocity) / time

Converting 90 mi/h to ft/s: 90 mi/h * (5280 ft/1 mi) / (3600 s/1 h)

= 132 ft/s

Converting 60 mi/h to ft/s: 60 mi/h * (5280 ft/1 mi) / (3600 s/1 h)

= 88 ft/s

Plugging in the values: acceleration = (88 ft/s - 132 ft/s) / (200 ft / 88 ft/s)

= -1.65 ft/s²

(b) To find the time it takes to reduce the speed to 55 mi/h, we can use the formula:

time = distance / speed

Converting 55 mi/h to ft/s: 55 mi/h * (5280 ft/1 mi) / (3600 s/1 h)

= 80.67 ft/s

Plugging in the values: time = 200 ft / 80.67 ft/s

= 2.48 s

(c) To find the time it takes to bring the car to a complete stop from 90 mi/h, we can use the same formula as part (b):

Converting 0 mi/h to ft/s: 0 mi/h * (5280 ft/1 mi) / (3600 s/1 h)

= 0 ft/s

Plugging in the values: time = 200 ft / 132 ft/s

= 1.51 s