Answer:
The only case when the car have a negative velocity and a positive acceleration is "A car that is traveling in the −x direction increasing in speed."
Step-by-step explanation:
The velocity of an object at a given time is defined as the rate of change of position of the object at that time.
The velocity of the object is positive if it is moving in positive direction and negative otherwise.
The acceleration of an object at a given time is defined as the rate of change of velocity of the object at that time.
The acceleration of the object is positive if its velocity is increasing and negative otherwise.
For the motion of the car, let's check all statements:
A car that is traveling in the −x direction at a constant 20 m/s.
The car is traveling in -x direction, it means its velocity is negative but the velocity is constant which means the acceleration is zero.
A car that is traveling in the −x direction decreasing in speed.
The car is traveling in -x direction, it means its velocity is negative and the speed is decreasing which means the acceleration is also negative.
A car that is traveling in the −x direction increasing in speed.
The car is traveling in -x direction, it means its velocity is negative and the speed is increasing which means the acceleration is positive.
Thus, it is the case when the car have a negative velocity and the positive acceleration.
A car that is traveling in the +x direction increasing in speed.
The car is traveling in +x direction, it means its velocity is positive and the speed is increasing which means the acceleration is also positive.
A car that is traveling in the +x direction decreasing in speed.
The car is traveling in +x direction, it means its velocity is positive and the speed is decreasing which means the acceleration is negative.