Physics 101 question

Question

At time t = 0 an object is traveling to the right along the ±x axis at a speed of 10.0 m􏰀s with acceleration –2.0 m􏰀s2. Which statement is true?

(a) The object will slow down, eventually coming to a

complete stop.

(b) The object cannot have a negative acceleration and

be moving to the right.

(c) The object will continue to move to the right, slowing

down but never coming to a complete stop.

(d) The object will slow down, momentarily stopping,

then pick up speed moving to the left.

Answer 1

Assuming the acceleration remains the same, answer d is correct. When acceleration has the opposite sign of velocity, velocity must eventually reach zero. Then if acceleration stays the same the object must begin accelerating in the reverse direction from the original. Velocity and acceleration are vectors, having a magnitude and a direction.

Answer 2

Keep in mind that the signs on the velocity and acceleration vectors, refer to the directions of the vectors. If the velocity and acceleration vectors are in the same direction, then the object is speeding up, while moving in the direction of the velocity. If the velocity and acceleration vectors are in opposite directions, then the object is slowing down, while moving in the direction of the velocity.

For example:

If an object has a positive velocity, and a positive acceleration, then it is moving in the positive direction, and speeding up.

If an object has a positive velocity, and a negative acceleration, then it is moving in the positive direction, and slowing down.

If an object has a negative velocity, and a negative acceleration, then it is moving in the negative direction, and speeding up.

If an object has a negative velocity, and a positive acceleration, then it is moving in the negative direction, and slowing down.

In this question, the velocity is +10 m/s, and the acceleration is -2 m/s², so the object is moving in the positive direction, and slowing down.

But what happens once it has slowed to zero velocity? There is still a negative acceleration, so will it remain at zero velocity, or will it start to speed up, now moving in the negative direction?