Applications of velocity-time graphs

The variation of velocity with time can be represented graphically to calculate acceleration exactly like we calculated speed from distance-time graph.

Let us now plot a velocity-time (v- t) graph for the following data.

Velocity in m/s	0	10	20	30	40	50
Time in seconds	0	2	4	6	8	10

Velocity - time graph

Take time along x-axis and velocity along y-axis.

Analyze the given data and make a proper choice of scale for x and y axes.

Plot the given points.

Consider any two points A and B on the straight-line graph.

Draw perpendiculars from A and B to x and y-axes.

Join A to C, ACB forms a right-angled triangle.

Calculations

Write the title and scale chosen for the graph.

Let us now see the nature of the v - t graph for the different types of motion.

Nature of v-t graph

Sub Topics

Applications of velocity-time graphs

Applications of velocity-time graphs

The following results can be deduced from velocity-time graph.

The acceleration produced in a body

The distance covered by a moving object

We can derive the equations of motion

Let us see how to calculate the distance covered by a moving object from speed-time graph.

The figure below gives the speed-time graph of a car moving with a uniform speed of 60kmp/hr for 5 hours.

Speed-Time graph of a car moving with a uniform speed

Distance traveled by the car (s) = v x t

But 60 km/h = BC = breadth of the rectangle OABC

5hr = OC = length of the rectangle OABC

i.e., the distance covered by the car = length x breadth = 300 km.

i.e., in order to calculate the distance covered by a moving object from a speed-time graph we just have to find the area enclosed by the speed-time graph and the time axis.

In case of non-uniform motion, the distance covered by the object cannot be found as the product of speed and time interval given by the speed-time graph because the speed does not remain constant throughout its motion. But, it is given by the area enclosed by the speed-time graph and the time axis.

The figure given below gives the motion of an object moving with variable speed.

Motion of an object moving with variable speed

The speed of the object is increasing in steps. The speed remains constant during the time interval 0 - t₁, t₁ - t₂, t₂ - t₃ ......

The total distance covered by the object during the time interval

0 ----> t₆ = Area of rectangle 1 + area of rectangle 2 +……+ area of rectangle 6.