What is Velocity Time Graph
It is used to show Velocity of object and Time Taken on a graph paper
Here,
Time Taken is shown on x axis
Velocity is shown on y axis
NoteIt is also called speed time graph(as velocity and speed are similar and used interchangeably)
Velocity-Time Graph for Uniform Speed
Suppose an object travels at Uniform velocity of 40 km/hour
It means
| Hour | Velocity |
| 0 | 40 |
| 1 | 40 |
| 2 | 40 |
| 3 | 40 |
| 4 | 40 |
Plotting it in Graph
We show
Time on x axis
Speed on y axis
Note
In this case,velocity time graph is in the form of Straight line parallel to x axis because speed of object does not change
(In our case,remains constant at 40 km/hour)
Velocity-Time Graph for Uniform Acceleration
Suppose an object travels at uniform acceleration of 20 km/hour
It means its speed is 20 km/hour in first hour,40 km/hour in second hour and 60 km /hour in third hour
So, his velocity will look like
| Hour | Velocity |
| 0 | 0 |
| 1 | 20 |
| 2 | 40 |
| 3 | 60 |
| 4 | 80 |
Note
In this case,velocity time graph is in the form of Straight line sloping upwards
Velocity-Time Graph for Non-Uniform Acceleration
Suppose an object travels at a velocity of 5 km/hour in first hour, 25 km/hour in second hour, 60 km/hr in third hour and 80 km/hour in fourth hour
| Hour | Velocity |
| 0 | 0 |
| 1 | 5 |
| 2 | 25 |
| 3 | 60 |
| 4 | 80 |
Note
In this case,velocity time graph is in the form of Curved line sloping upwards
Velocity-Time Graph for Uniform Retardation
Suppose an object travels at uniform retardation of 20 km/hour
If his speed is 80 km/hr in the beginning.
It means that its speed will be 60 km/hour in first hour, 40 km/hour in second hour and 20 km /hour in third hour
So, his velocity will look like
| Hour | Velocity |
| 0 | 80 |
| 1 | 60 |
| 2 | 40 |
| 3 | 20 |
| 4 | 0 |
Velocity-Time Graph for Non-Uniform Retardation
Sometimes velocity or speed of on object decreases
Suppose an object was traveling at a speed of 60 km/hour
its speed decreases to 40 km/hour in second hour and 20 km/hour in third year
| Hour | Velocity |
| 0 | 80 |
| 1 | 70 |
| 2 | 40 |
| 3 | 10 |
| 4 | 0 |
In this case,there is uniform retardation (or negative acceleration) of 20 km/hour
So distance time graph is in form of a straight line sloping downwards
How to Find Acceleration and Distance by Velocity Time Graph
Acceleration = Slope of v-t graph
Distance = Area under v-t graph bounded by its axes
How to find Distance travelled
Velocity Time Graph Summary
Questions
NCERT Question 5 - A driver of a car traveling at 52 km h–1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h–1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
NCERT Question 8 -
The speed-time graph for a car is shown is Fig. 8.12.
(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
