What is acceleration? When a body is not in a uniform motion, i.e. the body covers different distances in equal intervals of time, its velocity changes. The Body has different values of velocity at different instances and at different points of the path. This means that the change in velocity of the body, during any interval of time, is not zero

 

The rate of change of velocity of the body with respect to time is defined as the acceleration of the body. It measures the change in the velocity of the body per unit of time.

 

It is denoted by �a� If the initial velocity of a body at time t=0 is u and the final velocity of the body at time t= t is v. Then the acceleration a= (v-u)/t and it is expressed in meter/second²

 

Acceleration is a vector quantity

 

When a body is moving along a straight line with a uniform velocity, the change in its velocity = 0
Therefore the acceleration is 0. When the final velocity of a body increases as compared to its initial velocity in time �t', acceleration is taken to be positive and the direction of acceleration is along the direction of velocity and the motion is called an accelerated motion.

 

When the velocity of a body decreases with time, then the difference in final and initial velocity will be negative and therefore the acceleration will also be negative. The negative acceleration is also called retardation.

 

Uniform Acceleration

When the velocity of a body moving along a straight line, changes by equal amounts in equal intervals of time i.e. when the velocity of a body changes at a uniform rate, the body is said to have uniform acceleration e.g.:

 

� Motion of body falling freely under the action of gravity.
� Motion of a ball rolling down a smooth inclined plane.
� Motion of a bicycle going down the slope of a road when there is no pedaling and when the air resistance is neglected.

 

Nonuniform acceleration

 

When the velocity of a body changes at a non-uniform rate, i.e. velocity changes by unequal amounts in equal intervals of time, the acceleration of the body is said to be non-uniform.

 

Velocity- Time Graph

 

The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph. In this graph, the time is represented along the x-axis and the velocity is represented along the y-axis. Suppose a body is moving with a uniform velocity. Its graphical representation will be like�..

 

It will be a straight line parallel to x-axis i.e. its value will not change with time.

 

We know that velocity = displacement/time.

 

So, velocity * time = displacement

 

The product of velocity and time gives us the distance (or the magnitude of displacement) of the body. To calculate the magnitude of the displacement made by the car between t1 and t2, draw perpendicular lines from the points corresponding to the time t1 and t2 on the graph. The magnitude of displacement made by the body is equal to the area enclosed by the velocity-time graph and the time axis.

 

So, distance or ( magnitude of the displacement) is
S= AC * CD
= [(2.5 meter/second) * (t2-t1)seconds]
= 2.5 (t2-t1) meters
= area of the rectangle ABCD (shaded area)

 

Now let us analyze the scenario when the body moves with the uniform acceleration. Now let us consider the velocity-time graph of a car moving with uniform acceleration.

 

Now plot the velocity time graph for the same. The area under the velocity time graph gives us the distance of the car in a given interval of time. Since the magnitude of the velocity of the car is changing due to acceleration, the distance �s� of the car will be given by the area ABCDE under the velocity time graph i.e.

 

S= area ABCDE
= Area of rectangle ABCD + area of triangle ADE
= AB * BC + � (AD * DE)
Slope of the graph will give us the acceleration of the car. Take any two points on the graph.

 

Let the points be A and E. Draw lines perpendicular to X and Y axes from these two points.

 

Let us say that they meet on the y-axis at V2 and V1 and on the x-axis at t2 and t1. So the acceleration a= (v2-v1)/(t2-t1). Now observe these two velocity-time graphs carefully. What can you conclude from these graphs?

 

This velocity-time graph represents the motion of an object, whose velocity is decreasing with time because the acceleration is negative. This velocity-time graph represents the nonuniform variation of velocity of the object with time.

 

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