A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively.
(a = acceleration, v = velocity, x = displacement, t = time)
- (A), (B), (C)
- (A)
- (A), (B), (D)
- (B), (C)
The Correct Option is C
Solution and Explanation
At time $t$
$v = 0 + at \Rightarrow v = at$
also $x = 0(t) + \frac{1}{2} at^2 \; \Rightarrow \; x = \frac{1}{2} at^2$
Graph (A) ; (B) and (D) are correct.
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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.