What is the physical quantity represented by the tangent drawn to this graph?

Question

BlackTom AI · Accepted Answer

The graph shown has Velocity (ms^-1) on the vertical axis and Time (s) on the horizontal axis, so the curve represents how velocity changes with time.
Option a. Acceleration: The tangent to a velocity-time graph gives the rate of change of velocity with respect to time, which by definition is acceleration. Therefore the slope of that tangent corresponds to acceleration.
Option b. Speed: Speed is the magnitude of velocity. The tangent line does not directly represent magnitude; it represents how velocity is changing in time, i.e., acceleration, not speed.
Option c. Velocity: While the graph itself is a velocity-time graph, the tangent line to the graph does not “become” velocity; it describes the rate of change of velocity (acceleration). So this option is misleading.
Option d. Displacement: Displacement is the integral of velocity over time, i.e., area under a velocity-time curve, not something provided by a tangent to the curve. The tangent relates to instantaneous rate of change, not accumulated position.
In summary, the tangent to a velocity-time graph represents acceleration, since slope = dv/dt, the definition of acceleration.

What is the physical quantity represented by the tangent drawn to this graph?

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