Question

I'm so confused pls give steps!!!

Problem 4

You are driving at 75 mph on the freeway. You’ve been distracted by a text message on your phone

and when you look up you see all lanes of traffic are stopped ahead of you.

Yikes!

You slam on your brakes as hard as they will go. Fortunately, you stop just in time with no inches

to spare and avoid hitting the car ahead of you. You were driving your parents’ Prius which has a

stopping distance of 138 ft when traveling at 60 mph. You may assume this same deceleration

when you slam on the brakes at 75 mph.

a) Write an algebraic expression to find the deceleration. Do not evaluate this expression here.

b) How long are the skid marks you left?

c) How much time did it take to stop?

Answer 1

a) The deceleration can be found using the formula:

deceleration = (final velocity - initial velocity) / time

When slamming on the brakes, the final velocity is 0 mph, the initial velocity is 75 mph, and the time taken to stop is unknown. So, the algebraic expression for deceleration is:

deceleration = (0 - 75) / time

b) The stopping distance can be calculated using the formula:

stopping distance = (initial velocity)^2 / (2 * deceleration)

Substituting the given values of initial velocity and deceleration, we get:

stopping distance = (75)^2 / (2 * deceleration) = (75)^2 / (2 * (0 - 75 / time))

Simplifying this expression, we get:

stopping distance = 138 * 75 / 60 = 172.5 feet

So, the skid marks left are 172.5 feet.

c) The time taken to stop can be found by dividing the stopping distance by the initial velocity and then multiplying by 3600 to convert from hours to seconds. Using the same values as in part b), we get:

time taken to stop = stopping distance / initial velocity * 3600 = 172.5 / 75 * 3600 = 24.2 seconds

So, it took approximately 24.2 seconds to stop.