Question

At time $t=0$an object is travelling to the right along the + x axis at a speed of$10\mathrm{m}/\mathrm{s}$ with acceleration $-2.0\mathrm{m}/{\mathrm{s}}^2$. Which statement is true?

1. The object will slow down, eventually coming to a complete stop.
2. The object cannot have a negative acceleration and be moving to the right.
3. The object will continue to move to the right, slowing down but never coming to a complete stop.
4. The object will slow down, momentarily stopping, then pick up speed moving to the left.

Short answer

Option (d): The object will slow down, momentarily stopping, then pick up speed moving to the left.

Step-by-step solution

Step 1. Definition of negative acceleration

The rate of change of velocity of an object with respect to time is known as acceleration. Negative acceleration carries a negative sign as it is directed opposite to the velocity.

A graph between the velocity of an object at different time intervals is given below.

The object has a negative acceleration as the slope of the graph is negative.

Step 2. Identification of given data

Velocity of the object, $v=10\mathrm{m}/\mathrm{s}$

Acceleration of the object,$a=-2\mathrm{m}/{\mathrm{s}}^2$

The motion of the object is along the positive x-direction.

Step 3. Analysis of the motion of the object

If an object is moving with negative acceleration, its velocity becomes more and more negative. The deceleration remains constant, and the object comes to rest for an instant of time. It starts to travel again towards the left, i.e., in the opposite direction, with a greater velocity.

Thus, the object will momentarily halt and then pick up speed, moving to the left.