Distance and Average Velocity from Velocity Time Graph

To find the total distance travelled and the average velocity of the particle during the given time interval of $t = 0\text{ s}$ to $t = 40\text{ s}$, we analyze the velocity-time ($v$-$t$) graph.

1. Calculation of Total Distance Travelled

The total distance travelled by a particle is the sum of the absolute areas enclosed by the velocity-time graph and the time axis.

From the graph:

• First Region ($t = 0\text{ s}$ to $t = 20\text{ s}$): This forms a triangle above the time axis with a base of $20\text{ s}$ and a peak velocity of $+5\text{ m/s}$. $\text{Area}_1 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20\text{ s} \times 5\text{ m/s} = 50\text{ m}$

• Second Region ($t = 20\text{ s}$ to $t = 40\text{ s}$): This forms a triangle below the time axis with a base of $20\text{ s}$ and a trough velocity of $-5\text{ m/s}$. $\text{Area}_2 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20\text{ s} \times (-5\text{ m/s}) = -50\text{ m}$

The total distance travelled is the sum of the magnitudes of these areas: $\text{Total Distance} = |\text{Area}_1| + |\text{Area}_2| = 50\text{ m} + |-50\text{ m}| = 100\text{ m}$

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2. Calculation of Average Velocity

Average velocity is defined as the total displacement divided by the total time taken: $v_{\text{avg}} = \frac{\text{Total Displacement}}{\text{Total Time}}$

The total displacement is the algebraic sum of the areas under the $v$-$t$ graph: $\text{Total Displacement} = \text{Area}_1 + \text{Area}_2 = 50\text{ m} + (-50\text{ m}) = 0\text{ m}$

Thus, the average velocity is: $v_{\text{avg}} = \frac{0\text{ m}}{40\text{ s}} = 0\text{ m/s}$

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Conclusion

• Total Distance Travelled: $100\text{ m}$
• Average Velocity: Zero

Therefore, the correct option is C.