Question

A particle starts from origin 0 from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represented the motion qualitatively:
(a=acceleration, v=velocity, x=displacement, t=time)

A) A, B, C
B) A
C) A, B, C
D) B, C

Answer 1

Hint: Initial velocity describes how fast an object travels when gravity first applies force on the object. Velocity defines the direction of the movement of the body or the object. Acceleration is defined as the rate at which an object changes its velocity.

Step-By-Step answer:
Given initial velocity u=0 and acceleration is constant
At time t
v=0 + at
v=at
Also;
$ x = 0(t)\dfrac{1}{2}a{t^2} \Rightarrow x = \dfrac{1}{2}a{t^2} $
So in the given graph, (A);(B);(D) are the correct.
Therefore, the option (C) is the correct answer.

Initial velocity is the velocity, in the velocity of the object before acceleration causes a change. After acceleration for some amount of time, the new velocity is the final velocity.
Basically, at time (t=0), the initial velocity is zero. When the body starts from rest or it changes its direction of motion, it is known as initial velocity. We generally consider the initial velocity is equal to u=0, only when the object is at rest.
Acceleration is a vector quantity and moreover an object is said to an acceleration if it changes its velocity. Acceleration is a change in speed.

Note: The difference between velocity and acceleration is that the velocity can be defined as the rate of change of position with respect to time and acceleration is defined as rate of change of velocity. Velocity is in meters per second and acceleration is a meter per second squared.