True or False? (a) A car must always have an acceleration in the same direction as its velocity. (b) It’s possible for a slowing car to have a positive acceleration. (c) An object with constant nonzero acceleration can never stop and remain at rest.
The Correct Answer and Explanation is:
Answers:
(a) False
(b) True
(c) False
Explanation
Understanding the relationship between velocity and acceleration is crucial in physics, especially in kinematics. Here’s a detailed explanation of each statement:
(a) False:
A car does not need to have acceleration in the same direction as its velocity. Acceleration is the rate of change of velocity, not the same thing as velocity. If a car is slowing down, its acceleration is in the opposite direction to its velocity. This is known as negative acceleration or deceleration. For example, a car moving forward (positive velocity) but braking (acceleration pointing backward) is experiencing acceleration opposite to its direction of motion.
(b) True:
It is indeed possible for a slowing car to have a positive acceleration—this depends on the coordinate system or direction defined as positive. Suppose the car is moving in the negative direction (e.g., backward), and it slows down. Then the acceleration must be positive (opposite the motion) to reduce its negative velocity. Hence, even though the car is slowing, the acceleration could still be considered positive relative to the chosen coordinate system.
(c) False:
An object with constant nonzero acceleration can momentarily stop. A classic example is an object thrown vertically upward. As it rises, gravity (a constant downward acceleration) slows it down until its velocity becomes zero at the peak. At that instant, although the object is at rest (velocity = 0), it is still under the influence of a constant acceleration (gravity), so it resumes motion downward immediately after. Therefore, stopping momentarily is consistent with constant nonzero acceleration.
In summary, acceleration can differ in direction from velocity, can be positive even while slowing down, and does not prevent an object from stopping momentarily before changing direction.
