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:
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:
- $1: 2 $
- $1: 4$
- $1: 3$
- $1: 1$
The Correct Option is C
Approach Solution - 1
From the velocity-time graph, we calculate the displacement and total distance traveled:
- Displacement: The net displacement is the area under the graph considering direction: \[ \text{Displacement} = (16) + (-8) +16+ (-8) = 16 \, \text{m}. \]
- Distance: The total distance is the sum of the absolute areas under the graph: \[ \text{Distance} = |16| + |16| + |16| = 48 \, \text{m}. \]
The ratio of displacement to distance is:
\[ \frac{\text{Displacement}}{\text{Distance}} = \frac{16}{48} = \frac{1}{3}. \]
Approach Solution -2
The correct answer is (C) : \(1: 3\)
Displacement =Σ area =16−8+16−8=16m
Distance =Σ∣ area ∣=48m
Distance : displacement =3 : 1
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.