Question:
A particle moves along a straight line along the \(x\)-axis. Its position \((x)\) versus time \((t)\) graph is shown in the figure \([x \text{ in meters and } t \text{ in seconds}]\). Its average speed during the motion is:
A particle moves along a straight line along the \(x\)-axis. Its position \((x)\) versus time \((t)\) graph is shown in the figure \([x \text{ in meters and } t \text{ in seconds}]\). Its average speed during the motion is:
Show Hint
Average speed is calculated using:
\[
\text{Average speed}=
\frac{\text{Total distance travelled}}{\text{Total time taken}}
\]
Always use total distance, not displacement, while calculating average speed.
Updated On: Jun 25, 2026
- \(0.4\ \text{ms}^{-1}\)
- \(1.0\ \text{ms}^{-1}\)
- \(0.8\ \text{ms}^{-1}\)
- \(0.6\ \text{ms}^{-1}\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Read the coordinates from the graph.
From the graph, the motion of the particle is: \[ (0,1)\rightarrow (2,3)\rightarrow (3,3)\rightarrow (4,2)\rightarrow (5,3) \] Thus, the particle moves through the following positions: \[ x=1 \to 3 \to 3 \to 2 \to 3 \]
Step 2: Calculate the total distance travelled.
Distance from \[ x=1 \text{ to } x=3 \] is \[ |3-1|=2\ \text{m} \] Distance from \[ x=3 \text{ to } x=3 \] is \[ 0\ \text{m} \] Distance from \[ x=3 \text{ to } x=2 \] is \[ |2-3|=1\ \text{m} \] Distance from \[ x=2 \text{ to } x=3 \] is \[ |3-2|=1\ \text{m} \] Hence, total distance travelled is \[ 2+0+1+1=4\ \text{m} \]
Step 3: Calculate the total time taken.
Initial time: \[ t=0\ \text{s} \] Final time: \[ t=5\ \text{s} \] Therefore, \[ \text{Total time}=5\ \text{s} \]
Step 4: Calculate the average speed.
Average speed is defined as \[ \text{Average speed} = \frac{\text{Total distance travelled}}{\text{Total time}} \] Substituting the values, \[ \text{Average speed} = \frac{4}{5} \] \[ =0.8\ \text{ms}^{-1} \]
Step 5: Final conclusion.
Hence, the average speed of the particle is \[ \boxed{0.8\ \text{ms}^{-1}} \]
From the graph, the motion of the particle is: \[ (0,1)\rightarrow (2,3)\rightarrow (3,3)\rightarrow (4,2)\rightarrow (5,3) \] Thus, the particle moves through the following positions: \[ x=1 \to 3 \to 3 \to 2 \to 3 \]
Step 2: Calculate the total distance travelled.
Distance from \[ x=1 \text{ to } x=3 \] is \[ |3-1|=2\ \text{m} \] Distance from \[ x=3 \text{ to } x=3 \] is \[ 0\ \text{m} \] Distance from \[ x=3 \text{ to } x=2 \] is \[ |2-3|=1\ \text{m} \] Distance from \[ x=2 \text{ to } x=3 \] is \[ |3-2|=1\ \text{m} \] Hence, total distance travelled is \[ 2+0+1+1=4\ \text{m} \]
Step 3: Calculate the total time taken.
Initial time: \[ t=0\ \text{s} \] Final time: \[ t=5\ \text{s} \] Therefore, \[ \text{Total time}=5\ \text{s} \]
Step 4: Calculate the average speed.
Average speed is defined as \[ \text{Average speed} = \frac{\text{Total distance travelled}}{\text{Total time}} \] Substituting the values, \[ \text{Average speed} = \frac{4}{5} \] \[ =0.8\ \text{ms}^{-1} \]
Step 5: Final conclusion.
Hence, the average speed of the particle is \[ \boxed{0.8\ \text{ms}^{-1}} \]
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