Which of the following is true of an object with zero acceleration? a) It will maintain constant speed and direction. b) It will maintain constant circular motion. c) It will move along the trajectory of a projectile. d) It will change direction without changing speed. e) It will change speed without changing direction.
To address this question, we’ll need to define acceleration, understand what it means to have zero acceleration, and then apply that to the five-answer choices. The acceleration of an object is the rate of change of its velocity. The velocity of an object is a vector whose size is the speed of the object — how fast it’s going and whose direction is the direction of the object’s motion. When we talk about velocity changing, what we mean is either a change in the speed or in the direction. Let’s illustrate this, with two examples.
For the first example, we’ll start with the ball at one end of a straight track. The ball has an initial velocity pointing off to the right. And after some time the ball has made it to the other end of the track. In this example, the ball’s velocity is now different. Although the direction is still the same, the velocity is much larger. In other words, the speed has increased.
Now let’s consider a second example. An identical ball with the same initial velocity now moves along a curved track. Once the ball reaches the end of the track we’ll again give it a different velocity. This time, though, only the direction has changed, but the size has stayed the same. In both examples, the ball has accelerated. In the first example, the speed, the size of the velocity, has changed. In the second example, the direction of the velocity has changed. In both examples, the velocity has changed, so the ball has accelerated. Acceleration can also be a composite of these two. If in the second example, the velocity had gotten larger, then the acceleration would have resulted in both a changed direction and a changed speed.
Now that we understand acceleration, what does it mean to have zero acceleration? Zero acceleration means the rate of change of velocity is zero. So velocity stays the same; there’s no change. If velocity isn’t changing, then neither are its components. So speed and direction will also remain constant. Looking at the answer choices, we see that choice a) matches the properties of zero acceleration, maintaining constant speed and direction or no change in velocity. Choice a) is true. But let’s see why all the other choices are not true.
Choices d) and e) aren’t true just by the definition of acceleration. Choice d) has the object changing direction. Choice e) has the object changing speed. But both direction and speed are ways that the velocity can change. So an object that isn’t accelerating won’t be changing either of these, even if the other one stays constant. Choice b) has the same problem is choice d). An object undergoing constant circular motion maintains a fixed speed as it moves about the circle. But the direction is constantly changing to keep the object on the circular path. Thus, since the direction of motion is changing, such an object must have nonzero acceleration and b) is false.
In fact, there’s a special name for the acceleration present in constant circular motion. It’s called centripetal acceleration. Finally, an object following the path of a projectile changes both speed and direction as it moves. Since both components of velocity are changing, such an object clearly has nonzero acceleration and c) is false. In fact, we could have gotten rid of c) at the beginning by remembering that, to find the trajectory of a projectile, we have to take into account a nonzero gravitational acceleration. With that, we have shown that b), c), d), and e) are all false and a) is the only true answer choice.