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Difficulty: MediumMechanics and Motion

A test car travels along a flat, circular track at a constant speed of 20 m/s20\text{ m/s}. Which of the following statements correctly describes the velocity and acceleration of the car?

  1. A
    The velocity is constant because the speed does not change, meaning the car experiences zero acceleration.
  2. B
    The acceleration is zero because the vehicle's downward gravitational weight is fully balanced by the normal force from the road surface.
  3. The velocity is continuously changing because its direction of motion changes, producing an acceleration directed toward the center of the track.Answer
  4. D
    The velocity remains scalar because the distance units of the circular path remain constant over time.

Answer

The velocity is continuously changing because its direction of motion changes, producing an acceleration directed toward the center of the track.
Velocity is a vector quantity defined by both speed and direction of travel. When an object moves along a circular path at a constant speed, its direction changes at every instant. Because velocity changes whenever direction changes, the object undergoes centripetal acceleration directed radially inward toward the center of the circle.

Step-by-Step Solution

1
Distinguish between the physical definitions of speed and velocity.
Speed (20 m/s20\text{ m/s}) is a scalar representing magnitude, while velocity is a vector containing both magnitude and direction.
Clarifying vector vs. scalar quantities is required to evaluate motion along a curved trajectory.
2
Analyze the car's direction of travel on the circular track.
As the car follows the curve, the tangent direction of travel continuously turns.
A change in direction constitutes a change in the velocity vector, even when speed remains constant.
3
Determine the resulting acceleration.
Acceleration is the rate of change of velocity (a=Δv/Δta = \Delta v / \Delta t), directed inward toward the center (centripetal acceleration).
An unbalanced inward force is required to alter direction, creating non-zero acceleration.

Key Concept

Vector nature of velocity and centripetal acceleration in circular motion
Estimated Time:1m 0s
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Topics

Mechanics and Motion

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