In which of the following cases does a car have a negative velocity and a positive acceleration? a car that is traveling in the check all that apply. check all that apply.
a.+x direction decreasing in speed.
b.+x direction increasing in speed.
c.−x direction decreasing in speed.
d.−x direction increasing in speed.
e.−x direction at a constant 20 m/s.

c. -x direction decreasing in speed.

Explanation:

Using the equation of motion:

Vf = Vi + at

at = Vf - Vi

a = (Vf -Vi)/t

Where Vf is the final velocity of the car, Vi id the initial velocity of the car, a is the acceleration of the car and t the time take by the car travelling.

Assuming that the magnitude of Vf is greater than the magnitude Vi.

If the car is moving with an increasing speed in the negative x direction the velocity of the car Vf is negative. As a result from the equation it is clear that the acceleration of the car will be negative. However say the brakes are applied and the car is now moving in the negative x direction with a decreasing speed then the velocity of the car Vf is positive. As a result from the equation of motion it is clear that the acceleration will be positive.

Therefore the car is moving in the -x direction deacreasing in speed.