Fill-in the blank in the following sentence: “If the net force acting on an object is constant and non-zero, then the _ of the object is changing at a constant rate.”
a) displacement
b) acceleration
c) velocity
The correct answer and explanation is :
The correct answer is:
c) velocity
Explanation:
Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:
[
F = ma
]
where:
- ( F ) is the net force,
- ( m ) is the mass of the object, and
- ( a ) is the acceleration.
If the net force acting on the object is constant and non-zero, then the acceleration ( a ) remains constant. Since acceleration is defined as the rate of change of velocity with respect to time, a constant acceleration implies that the velocity of the object is changing at a constant rate.
Mathematically, acceleration is given by:
[
a = \frac{dv}{dt}
]
Since ( a ) is constant, integrating both sides with respect to time gives:
[
v = v_0 + at
]
where ( v_0 ) is the initial velocity. This equation shows that the velocity of the object increases (or decreases) linearly over time, meaning it changes at a constant rate.
Now, let’s analyze why the other options are incorrect:
- (a) Displacement: Displacement is the overall change in position of an object. It depends on velocity and time, but its rate of change is not necessarily constant when acceleration is present. Therefore, it is not the correct answer.
- (b) Acceleration: Since the net force is given as constant, the acceleration remains constant and does not change at a constant rate. Instead, velocity changes at a constant rate due to this constant acceleration.
Thus, the correct answer is velocity because a constant net force leads to a constant acceleration, which causes velocity to change at a constant rate.