We have learnt about what speed and velocity are and the difference between the two. Now, we will learn about the Speed-Time graphs and velocity time graphs.

**Speed – Time Graphs**

We know that the speed at a certain time is the magnitude of the velocity at that time. So we can follow equations of motion to draw speed time graphs.

**Case 1: Speed-time graphs with constant speed (zero acceleration)**

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

Speed-

As clear from the graph, the speed is constant (c) throughout the time interval. No matter how much the time changes, the speed will be c at every instant.

Example: If the acceleration of a particle is zero (0), and speed is constant say 5 m/s at t =0, then it will remain constant throughout the time.** **

**Case 2: Speed-time graphs with constant acceleration**

When the acceleration is constant, and the initial speed of the particle is zero, the speed 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 speed 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 initial speed is zero, the speed increases or decreases linearly. The slope of speed-time graph will give the magnitude of acceleration (k).

**Case 3: Speed-time graphs with increasing acceleration**

When the acceleration is increasing with time, the speed 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, speed 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 initial speed is zero, the speed-time graph will be a curve. The slope of speed-time graph at any instant (at a certain time) will give the magnitude of 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.

Stay tuned with BYJU’S to learn more about speed time graphs, motion graphs and much more.

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