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If the velocity-time graph of an object is curved, the object is moving with ___________.
Uniform velocity
Zero acceleration
Non-uniform acceleration
Uniform speed
Non-uniform acceleration
If the velocity-time graph of an object is curved, the rate of change of velocity is not constant. This indicates that the object is undergoing non-uniform acceleration, meaning the acceleration is changing over time.
If the velocity-time graph of an object is curved, the rate of change of velocity is not constant. This indicates that the object is undergoing non-uniform acceleration, meaning the acceleration is changing over time.
Think of driving a car where you constantly vary the pressure on the gas pedal; your speed changes erratically, resulting in a curved line on a speedometer record.
Curved = Change in Acceleration (C=C)
a=dtdvтАЛ тАФ Instantaneous acceleration is the derivative of velocity with respect to time.
╬Фv=тИлadt тАФ Change in velocity is the integral of acceleration over time.
Acceleration is defined as the slope of the velocity-time graph, calculated as a=dtdvтАЛ. When the graph is a straight line, the slope is constant, implying uniform acceleration. If the graph is curved, the slope varies at different points, proving that the acceleration magnitude or direction is changing over time.
A straight line in a v-t graph represents uniform acceleration.
A horizontal line (zero slope) in a v-t graph represents zero acceleration (uniform velocity).
A curved line represents non-uniform or variable acceleration.
The area under a v-t graph represents displacement.
Analyzing irregular vehicular traffic movement
Studying the motion of objects under non-constant forces
Uniform velocity means acceleration is 0.
Uniform speed implies constant magnitude of velocity but does not restrict direction changes.
Option B is incorrect because zero acceleration requires a horizontal straight line, not a curve.
C is correct тАФ a curved velocity-time graph implies that the slope, which represents acceleration, is changing continuously, signifying non-uniform acceleration.
Always remember that in graphical analysis: slope of position-time gives velocity, and slope of velocity-time gives acceleration.
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