PLEASE HELP How long will it take until the car's speed drops to 12.0 m/s?

[DrSmiles]

Homework Statement

A 1.54 m wide, 1.48 m high, 1600 kg car hits a very slick patch of ice while going 19.0 m/s. Air resistance is not negligible.
If friction is neglected, how long will it take until the car's speed drops to 12.0 m/s?
To 11.0 m/s?

Homework Equations

Kinematics equations, F=ma


3. solution
I have no idea how to solve this :-(
If you solve it, please explain WHY?

 

[Mattowander]

Draw a free body diagram. What are the forces acting on the car?

 

[baba89]

Dear student,

I understand that you are struggling with this problem. Let me guide you through the steps to solve it.

First, we need to understand what is happening in the problem. A car with certain dimensions and mass is moving at a speed of 19.0 m/s and hits a patch of ice. We also know that air resistance is not negligible.

Now, in order to find out how long it will take for the car's speed to drop to 12.0 m/s, we need to use the kinematics equations. Specifically, we will use the equation vf^2 = vi^2 + 2ad, where vf is the final velocity, vi is the initial velocity, a is the acceleration and d is the distance traveled.

Since we are neglecting friction, we can assume that the only force acting on the car is the air resistance. Therefore, we can use the equation F = ma to find the acceleration. We know the mass of the car (1600 kg) and we can calculate the force of air resistance using the equation F = 0.5 * p * v^2 * A, where p is the density of air, v is the velocity and A is the frontal area of the car.

Once we have the acceleration, we can plug it into the kinematics equation along with the initial velocity (19.0 m/s) and the final velocity (12.0 m/s). This will give us the distance traveled by the car before it reaches a speed of 12.0 m/s.

To find out how long it takes for the car to reach a speed of 12.0 m/s, we can use the equation t = (vf - vi)/a, where t is the time.

Similarly, we can use the same process to find the time it takes for the car to reach a speed of 11.0 m/s.

I hope this explanation helps you understand the problem better. If you still have any doubts, please let me know. It is important to understand the concepts behind the equations and how to apply them in different situations. Keep practicing and you will get better at solving problems like this. Good luck!