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:
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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.
Step 1: Identify the motion segments from the graph. From the position-time graph, the particle positions are: at $t=0$, $x=1$ m; at $t=2$, $x=3$ m; at $t=3$, $x=3$ m; at $t=4$, $x=2$ m; at $t=5$, $x=3$ m. Average speed uses total path length, not net displacement, so we track every direction reversal. Step 2: Compute the distance for each segment. Segment 1 ($t=0$ to $t=2$): $|3-1|=2$ m. Segment 2 ($t=2$ to $t=3$): $|3-3|=0$ m. Segment 3 ($t=3$ to $t=4$): $|2-3|=1$ m. Segment 4 ($t=4$ to $t=5$): $|3-2|=1$ m. Step 3: Sum all distances. \[ d_{\text{total}} = 2+0+1+1 = 4 \text{ m} \] Step 4: Find the total time. \[ t_{\text{total}} = 5 - 0 = 5 \text{ s} \] Step 5: Apply the definition of average speed. \[ v_{\text{avg}} = \frac{d_{\text{total}}}{t_{\text{total}}} = \frac{4}{5} = 0.8 \text{ ms}^{-1} \] Step 6: State the final answer. \[ \boxed{v_{\text{avg}} = 0.8 \text{ ms}^{-1}} \]
