Question

Does the object represented in FIGURE Q1.5 have a positive or negative value of a_y? Explain.

Short answer

The acceleration of the object has the same direction as the velocity.

Step-by-step solution

Step 1. To write the given information.

The object starts from the point with the initial velocity $\overrightarrow{v}$
Each point represents the position of the body with respect to time.
The greater the distance between the points, the greater is velocity.

Step 2. The difference between the initial velocity vi→and final velocity vf→ gives the change in velocity of the object. vf→-vi →=∆v→The change in velocity is nothing but the acceleration of the object. If the difference is negative, it suggests that the acceleration is in opposite direction to the velocity whereas if the difference is positive, then the direction of acceleration and velocity is in same direction.

In the figure given below, at point 2, the initial velocity is represented as $\overrightarrow{v}$and the final velocity is represented as$\overrightarrow{v_i}$.The difference in the velocity of the object is given by:
localid="1647930533324" $\overrightarrow{v_i}-\overrightarrow{v}=negative.$
Since, the difference between the velocities is negative, it implies that the acceleration$\overrightarrow{a_y}$of the object would be in opposite direction of the motion. Therefore, the acceleration$\overrightarrow{a_y}$ is in upward direction.
Similarly, at point 3, the difference in the velocity is given as
$\overrightarrow{v_f}-\overrightarrow{v_i}=negative.$
Therefore, the acceleration of the object would be in upward direction.