Based on the velocity-time plot shown in the figure, determine the...

The distance travelled by the particle is the total area under the velocity-time graph, taking all areas as positive.

Area above the time axis ($A_1$) from $t = 0$ to $t = 20\text{ s}$:
$A_1 = \dfrac{1}{2} \times 20 \times 5 = 50\text{ m}$

Area below the time axis ($A_2$) from $t = 20$ to $t = 40\text{ s}$:
$A_2 = \dfrac{1}{2} \times 20 \times |-5| = 50\text{ m}$

Total distance $= A_1 + A_2 = 50 + 50 = 100\text{ m}$

The displacement is the net area under the velocity-time graph, considering the signs.

Total displacement $= A_1 - A_2 = 50 - 50 = 0\text{ m}$

Average velocity is the total displacement divided by the total time taken.

Average velocity $= \dfrac{\text{Total displacement}}{\text{Total time}} = \dfrac{0}{40} = 0\text{ m/s}$