Imagine you are watching your favorite racer compete in a championship race on television. After several hours of driving, the cars are about to complete their final lap. But, your favorite racer is lagging behind a few drivers. So he peeks forward, and notices those few drivers racing their cars at their present speed. Would it be possible for him to race past them if he pushes the paddle harder to accelerate? Yes, by the virtue of acceleration we have witnessed it many times! Similarly, a ball thrown down from the top of a bridge becomes faster and faster due to downward pull of gravity, commonly called “acceleration due to gravity”. What is this “acceleration” and how do you define it?
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Acceleration basically is the measure of how fast the velocity is changing wrt time. It is a vector quantity having both direction and magnitude. Acceleration does not give any information regarding how fast a body is moving; rather it tells us how fast the velocity is changing.
The average acceleration over a time interval is defined as the change in velocity divided by time taken. Average acceleration , where V_{1} and V_{2} indicate instantaneous velocities at time t_{1} and t_{2}. From the above equation, it is clear that a change in velocity will always cause an acceleration.
In the following velocity time (v-t) graph, the average acceleration in the interval ba is equal to the slope of the graph between b and a.
Suppose an object is moving with variable acceleration, it will have different acceleration at different times. The instantaneous acceleration is defined as the change in velocity divided by time such that the limiting value of time approaches zero. If denotes the time interval, then and
The graphical meaning of at point p is the slope of the graph at point p. I.e the slope of the tangent drawn on the v-t curve at point p gives instantaneous acceleration.
Unit- m/s^{2}.
Dimension- [LT^{-2}]
When a body traveling in the +ve direction, as it speeds up, its acceleration is +ve
Eg. a car speeds up from 2 m/s to 4 m/s in 1 second then
When the same body slows down, its acceleration is -ve
Eg. A car slows down to 2 m/s from 4 m/s in 1 second then
When a body traveling in the -ve direction, as it speeds up, its acceleration is -ve
Eg. a car speeds up from -2m/s to -4 m/s in 1 second then
When the same body slows down, its acceleration is +ve
Eg. A car slows down to -2 m/s from -4 m/s , then
Velocity just gives information about how fast or slow an object is moving; but acceleration on the other hand gives us information about how fast velocity is changing–it has nothing to do with how fast a body moves.
Question 1. A car is traveling with a velocity of 20 m/s. After 10 second ,its velocity changes to 40 m/s. What is the average acceleration?
Answer:
Initial Velocity = 20 m/s
Final Velocity = 40 m/s
Elapsed time = 10 second
Average acceleration,
Question 2. A car is moving with a velocity of 30 m/s. The driver applied the brake for 5 second to bring it down to zero. What is the average acceleration?
Answer: Initial Velocity = 30 m/s
Final Velocity = 0 m/s
Elapsed time = 5 second
Average acceleration
Question 3. The velocity of an object as a function of time is given by . Find the instantaneous acceleration at t = 2 second.
Answer:
Instantaneous acceleration is
= 20 - 10t
Question 4. The - coordinate of a particle at any time are given by . Its acceleration is
(a) 4ms^{-2} (b)8ms^{-2} (c)20ms^{-2} (d)4oms^{-2}
Answer: (b)
Question 1. What is the SI unit of acceleration?
Answer: The SI unit of acceleration is m/s^{2}
Question 2.Is average acceleration a vector or scalar quantity?
Solution: Vector quantity since acceleration has both magnitude and direction.
Question 3.While in motion can a body have instantaneous acceleration as a negative value?
Solution: Yes it can be a negative if change in velocity is negative.
Question 4.Define Acceleration in mathematical terms.
Solution: Acceleration is mathematically defined as
indicates change in velocity and indicates change in time.