Question

The velocity and acceleration of an object at a certain instant are

v = (2.0 m/s)i + (3.0 m/s)j
a = (0.5 m/s²)i - (0.2 m/s²)j
At this instant, the object is
A) Speeding up and following a curved path.
B) Speeding up and moving in a straight line.
C) Slowing down and following a curved path.
D) Slowing down and moving in a straight line.

Answer 1

The object is decelerating and maintaining a straight path. The final answer is D, indicating slowing down and moving linearly.

Step-by-step explanation:

In this case, we can determine whether the object is speeding up or slowing down by considering the direction of the acceleration compared to the direction of motion. The object's velocity is given as 2.0 m/s in the x-direction and 3.0 m/s in the y-direction, while the acceleration is given as 0.5 m/s² in the x-direction and -0.2 m/s² in the y-direction. Since the acceleration in the x-direction is positive and the velocity in the x-direction is also positive, the object is speeding up in the x-direction. However, since the acceleration in the y-direction is negative and the velocity in the y-direction is positive, the object is slowing down in the y-direction.