Question

In which of the following cases does a car have negative velocity and a positive acceleration? A car that is travelling in the

1. –x direction at a constant $20\mathrm{m}/\mathrm{s}$.
2. –x direction increasing in speed.
3. +x direction increasing in speed.
4. –x direction decreasing in speed.
5. +x direction decreasing in speed.

Short answer

A car traveling in the –x-direction at a decreasing speed (option (d)) has a negative velocity and a positive acceleration.

Step-by-step solution

Step 1. Negative velocity and positive acceleration

An object that travels in a negative direction is said to have a negative velocity. The object can be accelerating if its velocity is changing. It can be slowing down with an acceleration (positive) in the opposite direction of motion.

Step 2. Defining the positive direction for the car’s motion

The car is moving along the x-axis. Suppose the positive x-direction for the motion of the car is towards the east. So, the negative x-direction will be towards the west.

Step 3. Analysis of the car’s motion 

For a negative velocity, the car has to travel towards the west. If the driver applies brakes and slows down, the velocity of the car changes (decrease). The acceleration is positive as it is directed in the opposite direction to the car’s motion.

Thus, a car traveling in the –x direction at a decreasing speed has a negative velocity and a positive acceleration.