Question:
The velocity ($v$) versus time ($t$) plot of a particle is shown in the figure,for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively :} 
The velocity ($v$) versus time ($t$) plot of a particle is shown in the figure,for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively :}
Updated On: Apr 12, 2026
- 25 m and zero
- 50 m and zero
- 100 m and zero
- 100 m and 2.5 m/s
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Total distance is the total area under the $|v|-t$ graph (all areas positive). Average velocity is total displacement divided by total time. Displacement is the algebraic sum of areas (above t-axis positive, below negative).
Step 2: Detailed Explanation:
From the graph:
Area 1 (0 to 20 s): Triangle with base 20 and height 5. Area $= \frac{1}{2} \cdot 20 \cdot 5 = 50 m$.
Area 2 (20 to 40 s): Triangle with base 20 and height $-5$. Area $= \frac{1}{2} \cdot 20 \cdot (-5) = -50 m$.
Total Distance $= |50| + |-50| = 100 m$.
Total Displacement $= 50 + (-50) = 0$.
Average Velocity $= \frac{\text{Displacement}}{\text{Time}} = \frac{0}{40} = 0$.
Step 3: Final Answer:
Distance is 100 m and average velocity is zero.
Total distance is the total area under the $|v|-t$ graph (all areas positive). Average velocity is total displacement divided by total time. Displacement is the algebraic sum of areas (above t-axis positive, below negative).
Step 2: Detailed Explanation:
From the graph:
Area 1 (0 to 20 s): Triangle with base 20 and height 5. Area $= \frac{1}{2} \cdot 20 \cdot 5 = 50 m$.
Area 2 (20 to 40 s): Triangle with base 20 and height $-5$. Area $= \frac{1}{2} \cdot 20 \cdot (-5) = -50 m$.
Total Distance $= |50| + |-50| = 100 m$.
Total Displacement $= 50 + (-50) = 0$.
Average Velocity $= \frac{\text{Displacement}}{\text{Time}} = \frac{0}{40} = 0$.
Step 3: Final Answer:
Distance is 100 m and average velocity is zero.
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