# Velocity-Time Graphs

We have learnt what velocity is. Now, we will learn about the Velocity-Time Graphs.

## Velocity-Time Graphs

To draw velocity-time graphs, we will use the three equations of motion.

### Case 1: Velocity-time graphs with constant velocity (zero acceleration)

When the velocity is constant, the velocity-time graph, with Y-axis denoting velocity and the X-axis denoting time, will be like:

• As the graph shows, the velocity is constant (c) throughout the interval.
• No particles of matter how much the time changes, the velocity will be c at every instant. In this case, we have taken the initial velocity to be positive.
• The graph will be different if the initial velocity is negative.
• Example: If the acceleration of a particle is zero (0), and velocity is constantly said 5 m/s at t =0, then it will remain constant throughout the time.

### Case 2: Velocity-time graphs with constant acceleration

• When the acceleration is constant (positive), and the initial velocity of the particle is zero, the velocity of the particle will increase linearly as predicted by the equation:
• v = u + at
• Since u = 0
• v = at

• As shown in the figure, the velocity of the particle will increase linearly with respect to time. The slope of the graph will give the magnitude of acceleration.
• Example: If the acceleration of a particle is constant (k) and is positive, the initial velocity is zero, and then the velocity increases linearly. The slope of the velocity-time graph will give the acceleration.

## Case 3: Velocity-time graphs with increasing acceleration

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• When the acceleration is increasing with time, the velocity-time graph will be a curve as predicted from the equation:
• v = u + at
• Since u = 0
• v= at
• Since acceleration is a function of time, the velocity-time graph will be a curve.
• Note: Since the acceleration continuously increases with time, the magnitude of the slope will also continuously increase with time.

• Example: If the acceleration of a particle is a function of time and the initial velocity is zero, the velocity-time graph will be a curve. The slope of the velocity-time graph at any instant (at a certain time) will give the acceleration at that time.
• Case 3 was just the case of increasing acceleration. There will be a different graph when the acceleration decreases with time. To learn more about velocity-time graphs, join BYJU’S.