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: Group the motion
Forward motion: $0$-$2$ s and $4$-$8$ s. Backward motion: $2$-$4$ s and $8$-$10$ s.

Step 2: Forward distance
$8\times2+4\times4=16+16=32$ m.

Step 3: Backward distance
$4\times2+4\times2=16$ m.

Step 4: Compute
Distance $=32+16=48$ m. Displacement $=32-16=16$ m. Ratio $=\frac{16}{48}=1:3$, option (D).

Final Answer:
Ratio of displacement to distance is 1:3. \[ \boxed{1:3} \]