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# Forces and Motion

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## Introduction to Motion

What if someone said that even if you are sitting completely still, you are in constant motion? Everything in the universe is in motion. The earth rotates around its axis and revolves around the sun, moving you constantly along with it. The proof of your movement is in reference to the sun or the moon or some other heavenly objects.

Imagine that you are in a moving train. When a person on the platform observes you, he sees you in motion. However, if you observe the person sitting next to you in the same train, he appears perfectly still with respect to you. Motion is determined by the difference between the positions of two objects or observers.

If you are in a moving car and there’s another car alongside, moving slightly faster than yours, you see a very small difference in motion with respect to your car or your position. Yet, both cars would appear as moving very fast to a stationary observer.

Every motion is in relation to some other place or object in the universe – it is with respect to a frame of reference. Every motion is an apparent motion with respect to that frame of reference.

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## What is Force?

An object at rest can only be put into motion by a cause. When you push a stationary cart, it starts to move. This cause, which changes the motion of an object, is Force. Force can cause an object to move, it can also cause an object to change direction, and it can cause an object to slow down and stop. When you hit a ball coming towards you, with a bat, you are applying force to change the direction of that ball. When you roll a ball on a rough carpet, it eventually slows down because the friction (a kind of force) between the carpet and the ball slows the ball down.

## Measuring Motion – Speed

Motion is determined in relation to time and distance, and is referred to as Speed. Speed determines how far an object has moved in a period of time. It is the Rate of Motion. A car that has moved 60 kilometers in an hour determines its speed. However, as the car would have moved at different speeds over the hour, starting from a position of rest (zero speed) and increasing its speed gradually so as to cover 60 kilometers in one hour, it is often referred to as Average Speed. It is a distance per time ratio.

Average Speed =Distance/Time

## Velocity

The calculation of speed is not bothered with direction of motion. If we speak of the motion of an object that is moving due south at 60 kilometers per hour, we are referring to the Velocity of the object. It has a magnitude (its speed) as well as a direction (south). Velocity refers to the displacement of a body rather than the distance traveled. It is a displacement per time ratio in a particular direction.

## Uniform and Non-Uniform Motion

When both the speed and direction of a moving object are constant, the motion of the object is said to be Uniform – it covers equal distance in equal intervals of time. A car that covers 30 meters in every second is said to have a uniform speed of 30 meters per second. An object that covers unequal distances in equal intervals of time is said to have Non-uniform motion. A horse that runs a race at different speeds at different points of time would be a good example.

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## Acceleration

If the velocity of an object changes (increases) from one time period to another, the object is said to have acceleratedhere Acceleration has occurred. Similarly, if the velocity has decreased from one time period to another, a Deceleration (or negative acceleration) is said to have occurred. A car which moves at 10 miles per hour for the first minute, then at 20 miles per hour for the second minute and finally at 30 miles per hour for the third minute, would have a Uniform Acceleration of “10 miles per hour per minute”. If the car slowed down at the same rate it would be a Uniform Deceleration. If the rates of acceleration or deceleration vary from one time period to another, then it is said to have Variable Acceleration or Variable Deceleration.

The formula to calculate acceleration is as follows –

 Acceleration= Final velocity – Starting velocity Elapsed Time

For example, if a car accelerates from 0 miles per hour to 60 miles per hour in 30 seconds then the acceleration of the car would be –

## Check Point

1) Use the formula for average speed to fill the missing values in the table:

 Average Speed Distance Time 1a ? 30 meters 30 seconds 1b 10 miles per hour 20 miles ? 1c 3 kilometers per minute ? 20 minutes

2) What is the average speed of a car that has traveled across 4 distances as below?

 Average Speed Distance Time Segment 1 Segment 2 Segment 3 Segment 4 30 miles 40 miles 25 miles 45 miles 1 hour 1 hour 1.5 hours 1.5 hours

3) Calculate the acceleration of a train which accelerates from 60 kilometers per hour to 120 kilometers per hour in 20 minutes.

1a)       Average speed is 1 meter per second

1b)       Time taken is 2 hours

1c)       Distance traveled is 60 kilometers

1. The average speed is 28 miles per hour
2. The acceleration is 3 kilometers per hour per minute

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