Question

In which of the following cases can the average velocity of a particle in a time-interval can be found by using geometry only given the velocity-time graphs?

• A. Velocity-time graph is a set of straight line with different slopes.
• B. Velocity-time graph is a straight line with constant slope and no discontinuities.
• C. Velocity-time graph is a set of straight lines with same slopes but with discontinuities.
• D. Average velocity can always be found by using geometry only.

Answer 1

The correct option is B Velocity-time graph is a straight line with constant slope and no discontinuities.

When v-t graph is a straight line with constant slope and no discontinuities,

$v_{avg}=\frac{v_2+v_1}{2}$

This value can be found from the graph by the following steps:

1. Mark A on the y-axis at the value $v_1$

2. Mark B on the y-axis at the value $v_2$

3. Draw the perpendicular bisector of AB cutting y-axis at P.

4. Then OP = average velocity

The above formula does not apply to any other conditions and average velocity in a given time interval cannot be found only with graph.