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If the velocity-time graph is curved (non-linear), the object is moving with _________.
Constant speed
Uniform acceleration
Constant rate of change of momentum
Non-uniform acceleration
Non-uniform acceleration
A non-linear (curved) velocity-time graph indicates that the slope of the graph, which represents acceleration, is changing continuously. Therefore, the object is undergoing non-uniform or variable acceleration.
A non-linear (curved) velocity-time graph indicates that the slope of the graph, which represents acceleration, is changing continuously. Therefore, the object is undergoing non-uniform or variable acceleration.
Think of a car driver pressing the accelerator pedal irregularly; as the car speeds up at fluctuating rates, the speedometer needle movement would trace a curved path on a graph.
CURVE = CHANGE: If the line curves, the rate of speed change is not constant.
a=dtdvтАЛ тАФ The instantaneous acceleration represented by the slope of the vтИТt graph.
╬Фv=тИлa(t)dt тАФ The total change in velocity for variable acceleration.
Acceleration is defined as the rate of change of velocity, given by the slope of the velocity-time graph: a=dtdvтАЛ. If the graph is a curve, the slope at different points is different, meaning the instantaneous acceleration a varies with time. This variation defines non-uniform acceleration.
A straight line on a vтИТt graph represents uniform (constant) acceleration.
A horizontal line on a vтИТt graph represents zero acceleration (constant velocity).
The area under a vтИТt graph represents total displacement.
A curved line signifies that the magnitude of acceleration is changing over time.
Analyzing motion of vehicles in dense, stop-and-go traffic.
Tracking the flight path of a projectile subject to variable air resistance.
Non-uniform acceleration occurs whenever the net force acting on a body is not constant.
Option B is incorrect because uniform acceleration requires a straight, non-horizontal line on a velocity-time graph.
D is correct тАФ A curved velocity-time graph implies that the slope (acceleration) is continuously changing over time.
Always remember: Slope of vтИТt graph = Acceleration, and Area under vтИТt graph = Displacement.
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