# Velocity – Time Graph of Various Types of Motions of a Particle

## Velocity – Time Graph of Various Types of Motions of a Particle

Particle is moving with a Constant Velocity: If a particle is moving with a constant velocity then, acceleration (a) is zero.

Let at any time velocity of the particle is u. Since, velocity remains constant so at any time velocity remains same. Hence, velocity – time graph for a particle moving with constant velocity is a straight line parallel to time axis.

Particle is moving with a Constant Positive Acceleration:

Equation to be used: v = u + at.

As the time passes, velocity goes on increasing. Hence, velocity – time graph for a particle moving with constant positive acceleration is a straight line inclined to time axis making an acute angle α. Here, tanα is the slope of the velocity – time graph.

Particle is moving with a Constant Negative Acceleration (Retardation):

Equation to be used: v = u + at.

As the time passes, the velocity goes on decreasing, at time t = t₀, velocity becomes zero and after that it increases in negative direction. Hence, velocity – time graphs for a particle moving with constant retardation is a straight line inclined to time axis making an obtuse angle α.

Since α is obtuse angle, hence slope tanα becomes negative. Hence, acceleration is negative.