Question

The velocity time graph of a body moving in a straight line is shown in a figure. The ratio of displacement to distance travelled by the body in time \(0\) to \(10\) s is

• A. \(1:1\)
• B. \(1:4\)
• C. \(1:2\)
• D. \(1:3\)

Hint:

Displacement is the signed area under the v-t graph and distance is the sum of absolute areas.

Answer 1

The Correct Option is D

Step 1: Read the graph
The v-t graph is made of rectangles. From 0 to 2 s, \(v=+8\) m/s. From 2 to 4 s, \(v=-4\) m/s. From 4 to 8 s, \(v=+4\) m/s. From 8 to 10 s, \(v=-4\) m/s.

Step 2: Rule
The signed area under a v-t graph gives displacement. The sum of the absolute areas gives distance travelled.

Step 3: Areas
\(A_1=8\times2=16\) m. \(A_2=-4\times2=-8\) m. \(A_3=4\times4=16\) m. \(A_4=-4\times2=-8\) m.

Step 4: Displacement and distance
Displacement \(=16-8+16-8=16\) m. Distance \(=16+8+16+8=48\) m.

Step 5: Ratio
\[ \frac{\text{displacement}}{\text{distance}}=\frac{16}{48}=\frac{1}{3} \] So the ratio is 1:3. A ratio of 1:1 would mean no reversal of direction, which is not the case, and 1:2 or 1:4 do not match the areas.

Final Answer:
The ratio is 1:3, option (D). \[ \boxed{1:3} \]