An object moving under a constant non-zero acceleration will:
a) Have their position change linearly
b) Have their position change quadratically
c) Have constant velocity
d) First stop then keep going in the same direction
e) determine without more information
The Correct Answer and Explanation is :
Correct Answer:
b) Have their position change quadratically
Explanation:
When an object moves under a constant, non-zero acceleration, its motion follows the kinematic equations of motion, which describe the relationships between displacement, velocity, acceleration, and time.
The position ( x(t) ) of an object moving under constant acceleration is given by the kinematic equation:
[
x = x_0 + v_0 t + \frac{1}{2} a t^2
]
where:
- ( x_0 ) is the initial position,
- ( v_0 ) is the initial velocity,
- ( a ) is the constant acceleration,
- ( t ) is the time.
Why is the Position Quadratic in Time?
The presence of the ( t^2 ) term in the equation means that the position follows a quadratic function over time. This quadratic relationship results from the fact that the velocity of the object is changing at a constant rate due to the acceleration.
Why Not the Other Options?
- (a) Position changing linearly → Incorrect because linear motion occurs only with constant velocity, not constant acceleration.
- (c) Constant velocity → Incorrect because velocity is constantly changing when there is acceleration.
- (d) First stop then keep going in the same direction → This would happen if the object had an initial velocity in the opposite direction of acceleration, but it’s not a general rule for all objects under constant acceleration.
- (e) Need more information → Incorrect since we know that the acceleration is constant and nonzero, which is sufficient to determine the quadratic nature of position.
Thus, the position of an object moving under constant acceleration follows a quadratic function over time.
Here is the generated illustration depicting an object moving under constant acceleration with a quadratic position-time curve. Let me know if you need any modifications or additional explanations!