We have learnt what velocity is. Now, we will learn about 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 X-axis denoting time, will be like:

As clear from the graph, the velocity is constant (c) throughout the time 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 say 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**

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, velocity-time graph will be a curve.

Note: Since the acceleration is continuously increasing 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 is decreasing with time. To learn more about velocity time graphs, join BYJU’s.

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