How Does Constant Acceleration Affect a Car's Motion When Braking?

[dandy9]

Homework Statement

When a car skids after applying its brakes, the acceleration of the car is in the opposite direction to the velocity of the car. If the acceleration of the car would remain constant in this direction, the car would do which of the following?

a) never stop but continue to speed up in the forward direction
b) eventually stop and then start to speed up in the forward direction
c) eventually stop and then start to speed up in the reverse direction
d) eventually stop and remain stopped

The Attempt at a Solution

I think the answer is d. My logic is that since the velocity vector and the acceleration vector are pointing in opposite directions, and the car is applying its brakes, the velocity is decreasing. Even the acceleration is constant, then the car will eventually stop because the velocity will reach zero if the brakes are being put on. Could someone please verify this? Am I right?

 

[vela]

It would stop, but would it remain stopped?

 

[dandy9]

the answer was
c) eventually stop and then start to speed up in the reverse direction

I think this is because even though the car will stop because the acceleration vector and velocity vector are pointing in opposite directions, the car will go in reverse because the acceleration vector is a constant force that keeps pulling at the car... I'm not really sure if I really understand this... If anyone cares to clear it up for me that would be great!

 

[vela]

That's essentially right, though acceleration itself isn't a force. You'll soon learn Newton's 2nd law, which says acceleration is caused by a net force on an object.

Note in this case, the constant acceleration can't be due to the brakes since once the car came to a stop, the brakes would no longer exert a force on the car. A better example would be when you throw an object straight up into the air. Initially, the velocity of the object and the acceleration due to gravity point in opposite directions, so the object slows as it rises. Eventually, at the highest point, it has come to rest. Gravity is still pulling down on the object, however, so now it reverses direction and falls back to the ground with increasing speed.

 

[rwisz]

Yes, you are correct. The correct answer is d) eventually stop and remain stopped. This is because the acceleration is always acting in the opposite direction of the velocity, so it will continue to slow down the car until it comes to a complete stop. If the acceleration were to remain constant, the car would eventually stop and remain stopped. This is because the acceleration is always acting in the opposite direction of the velocity, so it will continue to slow down the car until it comes to a complete stop. It will not start to speed up in the forward or reverse direction because the brakes are still applied, causing a constant deceleration.