A.1.5—Instantaneous and average values

Average values use an interval

Average speed is total distance divided by total time. Average velocity is displacement divided by elapsed time. Average acceleration is change in velocity divided by elapsed time.

Instantaneous values use one moment

Instantaneous velocity is the tangent gradient on a position–time graph; instantaneous speed is its magnitude and is what an ideal speedometer reports. Instantaneous acceleration is the tangent gradient on a velocity–time graph. Average values instead use a finite interval.

Connect graph quantities

The gradient of a velocity–time graph is acceleration, and the area under it is displacement. A constant acceleration therefore produces a straight-line velocity–time graph.

Common trap

Do not use the average gradient when a question asks for an instantaneous value. Use the tangent at the specified time.

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The graph shows the variation of the acceleration a with time t of an object moving in a straight line.

Which graph shows the variation of the velocity v of the object with time t ?

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

$v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as$

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.

A.1.5—Instantaneous and average values

Distinguish Instantaneous and Average Motion

Retrieve the A.1 Kinematics Model

A.1.5 Exam Analysis