Question

From the v - t graph shown, the ratio of distance to displacement in 25 s of motion is:

• A. \( \frac{3}{5} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{2}{5} \)
• D. \( \frac{1}{3} \)

Hint:

When finding distance, always consider the absolute value of the displacement, i.e., sum the areas without sign.

Answer 1

The Correct Option is C

Displacement is the area under the graph and distance is the total area covered, including all positive and negative regions of the graph.
Displacement = Area of graph with sign \[ = \left(\frac{1}{2} \times 10 \times 5 \right) + \left(10 \times 5 \right) = 25 + 50 = 75 \, \text{m} \] Distance = Area of graph with positive value \[ = \left(\frac{1}{2} \times 5 \times 20 \right) + \left(5 \times 20 \right) = 25 + 50 = 250 \, \text{m} \] Now, the ratio of distance to displacement is: \[ \frac{250}{75} = \frac{2}{5} \] Thus, the ratio is \( \frac{2}{5} \).