One of the most difficult things to learn in physics is that our everyday language is not always precise enough. For instance, we might say a car is “slowing down”, but that only gives us information about velocity, not its acceleration.
What can we say about the velocity of a car which has negative acceleration in the x-direction?
a. It is slowing down.
b. The x-component of its velocity is decreasing.
c. The x-component of its velocity is negative.
d. It is speeding up.
e. The x-component of its velocity is positive.
f. The x-component of its velocity is increasing.
The correct answer and explanation is :
The correct answer is:
b. The x-component of its velocity is decreasing.
Explanation:
To understand this, we need to distinguish between velocity and acceleration and how they relate to each other.
- Velocity is the rate at which an object changes its position in a specific direction. It is a vector quantity, meaning it has both magnitude (speed) and direction. In this problem, we are concerned with the x-component of velocity, which describes how the car is moving along the x-axis.
- Acceleration is the rate at which the velocity changes. It is also a vector quantity. If an object has negative acceleration in the x-direction, it means the car’s velocity is decreasing in the positive x-direction, or increasing in the negative x-direction, depending on the direction of its motion.
Now, let’s break down the choices:
- a. It is slowing down.
This statement is not necessarily true. Slowing down refers to a decrease in speed, but the car might actually be speeding up in the negative direction (if it was initially moving in the positive direction), so we cannot conclude this definitively. - b. The x-component of its velocity is decreasing.
This is the correct answer. If the car has negative acceleration in the x-direction, it means that the velocity along the x-axis is decreasing. If the car is moving in the positive x-direction, a negative acceleration will reduce its velocity. If the car is already moving in the negative x-direction, the negative acceleration will make the velocity more negative, i.e., it is still decreasing in magnitude but becoming more negative. - c. The x-component of its velocity is negative.
This is not necessarily true. The car’s velocity could be positive or negative initially. Negative acceleration in the x-direction would cause a change in the velocity, but we cannot definitively state that the velocity is negative without more context. - d. It is speeding up.
This is incorrect. Speeding up would happen if the acceleration is in the same direction as the velocity. Since the acceleration is negative, it would slow down the car, not speed it up. - e. The x-component of its velocity is positive.
This is not necessarily true. The car could be moving in the positive or negative x-direction initially, so the velocity component could be either positive or negative. - f. The x-component of its velocity is increasing.
This is incorrect. Negative acceleration means the velocity is decreasing in the positive x-direction or becoming more negative in the negative x-direction.
Thus, b is the most accurate and precise statement, as negative acceleration in the x-direction leads to a decrease in the x-component of the car’s velocity.