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# Acceleration

Suppose you are driving a car, and you are merging onto a freeway, you tend to go faster and eventually your speed increases. So the moment you speed up to fit into the flow of traffic, you are accelerating. Interesting, isn’t it? Let us know more about acceleration.

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Introduction to Motion
Distance, Displacement, Speed and Velocity
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## Acceleration

It is the rate of change of velocity with time. The only two ways to accelerate is by changing the speed or change in direction or change both. It is a vector quantity. If the velocity of the object increases with time, its acceleration increases. If the velocity of an object decreases with time, its acceleration is negative.

The motion is uniformly accelerated motion or it non-uniformly accelerated, depending on how the velocity changes with time. It is uniform for a body if the velocity changes by equal amounts in equal intervals and if its velocity changes by unequal amounts, it is non-uniform.

Acceleration=  $$\frac{Change in velocity}{time taken}$$

Its unit is m/s²

Constant speed does not guarantee that acceleration is zero. For example, a body moving with constant speed in a circle changes its velocity every instant and hence its acceleration is not equal to zero.

Velocity is a quantity having both magnitude and direction, a change in velocity may involve either or both of these factors. Acceleration may result from a change in speed, a change in direction or changes in both. Like velocity, acceleration can also be positive, negative or zero.

### Motion in Different Acceleration for Different Time Intervals

Let’s understand this through an example. Suppose, a particle started its motion from rest with an acceleration of 1m/s² for 2s and then continued it for next 1s changing to 2m/s². The distance travelled during this will be:

After 2s the velocity is, v = u+at = 2 m/s

Now, if this is the initial velocity for the second half of the motion, s2=ut+(1/2)at² =3 m

Distance traveled in first half is: s= 0+(1/2)at² = 2 m

Hence total distance traveled = s1+s= 5 m

## Average Acceleration

It is the change in velocity divided by an elapsed time. For instance, if the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s². This means that the marble’s velocity will increase by 20 cm/s every second.

It is the rate of change of velocity with respect to displacement

Acceleration is a = dv/dt

∴ a = dv/(dx/v)

a = v(dv/dx)

Freefall object experiences an acceleration of g= 9.8m/s² in a downward direction that is towards the center of the earth. In upward direction it is -g = -9.8m/s²

### Acceleration of the Velocity-Time graph

In the given graph, a =  (40-20)/(4-2) = 10 m/s2. For a particle it is equal to the slope of a velocity-time graph.

## Solved Example For You

Q. A stone of mass m is thrown straight upward from the top of a multi-story building with an initial velocity of +15 m/s. Find out the acceleration of stone just after it is thrown?

1. Zero
2. 10m/s² downward
3. 15m/s² upward
4. 15m/s² downward

Answer: B. A body in the air always experiences a gravitational force in a downward direction. Thus the body is in the downward direction with a constant magnitude.

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