Question

The velocity-time graph of a body moving in a straight line is shown in the figure.

The ratio of displacement to distance travelled by the body in time 0 to 10s is:

• A. $1: 2 $
• B. $1: 4$
• C. $1: 3$
• D. $1: 1$

Answer 1

The Correct Option is C

The velocity-time graph depicts the velocity of a body moving in a straight line over a period from 0 to 10 seconds. We need to determine the ratio of displacement to the distance traveled by the body in this time interval. 

Let's break down the velocity-time graph into segments and calculate both displacement and distance.

1. The graph is divided into five intervals:
   1. 0 to 2 sec: Velocity = 8 m/s. Displacement = Distance = Area of rectangle = \(8 \times 2 = 16\) m.
   2. 2 to 4 sec: Velocity = -4 m/s. Displacement = Distance = Area of rectangle = \((−4) \times 2 = -8\) m.
   3. 4 to 6 sec: Velocity = 4 m/s. Displacement = Distance = Area of rectangle = \(4 \times 2 = 8\) m.
   4. 6 to 8 sec: Velocity = 6 m/s. Displacement = Distance = Area of rectangle = \(6 \times 2 = 12\) m.
   5. 8 to 10 sec: Velocity = -6 m/s. Displacement = Distance = Area of rectangle = \((−6) \times 2 = -12\) m.
2. Calculate the total displacement by adding the areas considering direction:
3. Calculate the total distance traveled by adding the absolute values of each segment (or areas):
4. Calculate the ratio of displacement to distance:

Thus, the ratio of displacement to distance traveled is \(1:3\).

The correct answer is: \(1:3\)