Respuesta :
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."
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.
[tex]\vec v = \dfrac{\text d\vec r}{\text dt}.[/tex]
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.
[tex]\vec a = \dfrac{\text d\vec v}{\text dt}.[/tex]
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.
