Car's Acceleration Into Gusting Wind

[Pat.Foop]

Homework Statement

A 2500kg car is traveling 35mph into a head wind gust of 28mph. The wind gust lessens to 16mph. How many seconds will it take for the car to reach velocity of 50mph assuming the force applied to the accelerator throughout remains unchanged?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Welcome to PF.

How would you think to approach this?

 

[nlightner]

I would first calculate the net force acting on the car due to the wind gust. Using the formula F=ma, where F is the net force, m is the mass of the car (2500kg), and a is the acceleration, I would first calculate the initial net force as F1 = 2500kg * (35mph - 28mph) = 17500kg*mph.

Next, I would calculate the final net force after the wind gust lessens to 16mph. Using the same formula, F2 = 2500kg * (35mph - 16mph) = 47500kg*mph.

Since the force applied to the accelerator remains unchanged, we can assume that the acceleration of the car remains constant throughout the whole process. Therefore, we can use the formula v = u + at, where v is the final velocity (50mph), u is the initial velocity (35mph), a is the acceleration, and t is the time.

We can rearrange the formula to solve for t, and we get t = (v-u)/a. Plugging in the values, we get t = (50mph-35mph)/a. To find the acceleration, we can use the formula a = F/m, where F is the net force and m is the mass of the car. Plugging in the values, we get a = (47500kg*mph)/2500kg = 19mph.

Therefore, t = (50mph-35mph)/19mph = 0.789 seconds. It will take the car approximately 0.789 seconds to reach a velocity of 50mph assuming the force applied to the accelerator remains unchanged.