Mathematics

Problem

A body moves along the X-axis such that its displacement from the origin at time

t

seconds is given by

x = 5t^{2} - 2t + 1\;\text{metre}.

Answer the following: (a) Find the instantaneous velocity of the body at

t = 2\,\text{s}

. (b) Find the instantaneous velocity at

t = 4\,\text{s}

. (c) Calculate the average velocity of the body between

t = 2\,\text{s}

and

t = 4\,\text{s}

and compare its magnitude with the instantaneous velocities obtained in parts (a) and (b).

Intuitive explanation

Instantaneous velocity is the rate of change of position at a specific moment—found by taking the derivative of the displacement function. Average velocity, by contrast, measures the total change in position over an interval divided by the time elapsed. By comparing these two quantities, you'll see how velocity can vary throughout a journey and why the average often falls between the instantaneous values at the endpoints.

Intuitive explanation

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