## Linear Motion

Background

In everyday life, we have observed bodies moving in various manners such as linear, circular, oscillatory among others. When a body moves in a straight line, it is said to be in linear motion.

Background

In everyday life, we have observed bodies moving in various manners such as linear, circular, oscillatory among others. When a body moves in a straight line, it is said to be in linear motion.

OBJECTIVES

#### By the end of this topic, you should be able to:

- Define the terms: distance, displacement, speed, velocity and acceleration
- Perform simple experiments to determine velocity and acceleration
- Determine acceleration due to gravity
- Plot and explain motion-time graphs
- Solve numerical problems in linear motion

Introduction

In this topic, we are going to learn about the common terms associated with linear motion, what happens when a body speeds up or slows down, what happens when a body falls freely due to the earth's gravity, plotting and explaining motion-time graphs.

Distance

Distance is defined as the total length of the path followed by a body. It is a scalar quantity since it lacks direction. Play the animation below to see the lacking aspect of direction in distance.

Displacement

Displacement is the distance covered by a body in a specified direction. Click the play button to observe a body undergoing a displacement.

Speed

Speed is the rate of change of distance. It is a scalar quantity (it lacks direction). The animation below illustrates the missing aspect of direction. Click on the play button and make your observations.

Velocity

Velocity is the rate of change of displacement or the speed of a body in a specified direction. Click the play button on the animation below and observe how the particle moves

.

Determination of velocity

A body can take different durations to cover the same distance, for example, a distance of 100m. When the time taken is shorter, the car is seen to move faster hence having a higher velocity.This velocity can be calculated by taking the ratio of the distance, d to the time taken, t in that specific direction. This means velocity, v equals to displacement, d divided by the time taken, t. Play the animation below and make your observations.

Acceleration

Acceleration is the rate of change of velocity. A negative acceleration is known as deceleration or retardation. Play the animation below to observe an accelerating body.

Determination of acceleration using the mathematical calculation method

To determine the acceleration of a moving body, we shall take a car moving between points A to B through X. Click on the animation below to observe this.

Observation

From the experiment, the car takes an average time of 7.5 seconds for its velocity to change from 5m/s to 10m/s.

Discussion

Acceleration of the car will be taken as the ratio of the change in velocity to the time taken for the change which equals to 0.76m/s2

Determination of acceleration due to gravity 'g'

This can be done by timing a steel ball bearing falling freely due to gravity from height, h metres in a time of t seconds. To determine the acceleration due to gravity 'g', we shall use the second equation of linear motion

S = ut + 1/2at2.

Since u = 0 m/s and S = h, and 'a' equals to 'g'

Therefore 'g' = 2h divide by t2 = 10/1.42 = 10.2m/s2

The ticker timer

The ticker timer can also be used to determine the acceleration of a body. It is a device that is electrically operated. When operating with the alternating current (a.c), its frequency is usually 50 Hertz meaning that it makes 50 dots per second. Play the video below to observe how a ticker timer works.

Motion-time graphs

We can also use graphical methods to describe the motion of a given body. The following are a few examples of such graphs.

Displacement-time graphs

We will discuss several types of displacement-time graphs under this including bodies which are stationary, bodies moving with; uniform velocity, increasing and decreasing velocities.

Case 1: A body moving with a constant velocity

In this case, the displacement of the body changes uniformly at equal time intervals. Play the animation below to observe this. From a displacement-time graph, gradient (slope) can be calculated which is equal to the velocity of the body whose motion is displayed by the graph. Play the animation below to observe this.

CASE 2: A stationary body

For this case, time is changing but displacement is not changing. The gradient of the graph gives a constant value of zero meaning that the velocity of the body is zero. Play the animation below to observe this.

CASE 3: A body moving with an increasing velocity (accelerating).

To determine the velocity of the body at any given time, a tangent is drawn at that point and the gradient of the tangent is calculated.

Obtaining the gradient from the graph

Click on the play button to observe how the gradient from this graph is obtained.

CASE 4: A body moving with a decreasing velocity (decelerating).

When the rate of change of displacement keeps on decreasing as time goes by, the body is said to be moving with decreasing velocity (decelerating).

Velocity-time graphs

Velocity-time graphs are illustrated in the following graphs.

CASE 1: Uniform velocity, uniform acceleration & uniform deceleration

In this illustration, we have graphs for uniform velocity, uniform acceleration and deceleration as labeled.

CASE2: Increasing acceleration.

Click on the word INCREASING ACCELERATION to observe the graph showing this.

CASE 3: Decreasing acceleration (deceleration).

Click on the word DECREASING ACCELERATION to observe the graph showing this.

**N.B. It should be noted that the area under a
velocity-time graph gives the displacement **

**undergone by the body.**

.

Linear Motion

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Linear Motion

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