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Difficulty: EasyMechanics and Motion

A delivery van travels along a circular entrance ramp at a constant speed of 25 mph25\text{ mph}. Why is the vehicle considered to be accelerating even though the speedometer reading remains unchanged?

  1. A
    The van's weight decreases as gravitational pull weakens around the curve.
  2. B
    The speedometer records distance in miles rather than standard metric units.
  3. The direction of travel is constantly changing, which alters the vehicle's velocity.Answer
  4. D
    Speed is a vector quantity that automatically increases whenever an object turns.

Answer

The direction of travel is constantly changing, which alters the vehicle's velocity.
Acceleration is defined in physics as the rate of change of velocity over time. Because velocity is a vector quantity consisting of both speed and direction, an object traveling in a circle is continuously changing its direction. This continuous change in direction means the velocity vector is changing, which produces acceleration directed toward the center of the turn.

Step-by-Step Solution

1
Define the relationship between speed, velocity, and acceleration
Speed is a scalar quantity (magnitude only), whereas velocity is a vector quantity (both magnitude and direction). Acceleration (aa) is the rate of change of velocity: a=ΔvΔta = \frac{\Delta v}{\Delta t}.
Determining whether an object is accelerating requires evaluating its velocity vector rather than just its scalar speed.
2
Analyze the motion of the vehicle on a curved path
Although the magnitude of the velocity (speed) is steady at 25 mph25\text{ mph}, the direction of travel continuously turns along the curve.
A change in the direction of a vector constitutes a change in velocity.
3
Conclude whether acceleration occurs
Because velocity changes continuously with direction, the vehicle undergoes centripetal acceleration directed toward the center of the curve.
Any non-zero change in velocity over time confirms acceleration.

Key Concept

Velocity is a vector quantity comprising both magnitude and direction; thus, changing direction at constant speed results in acceleration.
Estimated Time:45s
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Topics

Mechanics and Motion

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