TECHNICIAN SCIENCECHAPTER 3 : LINEAR MOTION

UNDERSTANDING LINEAR MOTIONDefine distance and displacementDefine speed and velocityDefine acceleration and decelerationCalculate speed, velocity and acceleration/decelerationSolve problem on linear motion using the equation of motionDetermine distance, displacement and velocity from a displacement-time graphDetermine distance, displacement, velocity and acceleration from a velocity-time graph

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LINEAR MOTION*Linear motion is referred to as motion along a straight line pathCONCEPTUAL MAP

Distance and Displacement*

DistanceDisplacementDistance is the total path length traveled from one location to another.Displacement is the distance between two locations measured along the shortest path connecting them, in a specified direction.Distance is a scalar quantity. It has magnitude but no direction.Displacement is a vector quantity. It involves both magnitude and direction The SI unit of distance and displacement is meter (m)

EXERCISE 1*A student drive his motorcycle to shop, on the way to his schoola) What is the distance he had to drive to reach to his school?b) What is the displacement of the school from the house?

After school the student drove back to his house without crossing the shop.c) what is the total distance he had to drive to reach back to his house?d) what is the total displacement he drove back to his house?5 km6 km8 kmhouseshopschool

Speed is the distance traveled per unit time.Speed can also be define as the rate of change of distance.The average speed of a body is calculated by:

Speed = Distance traveled, s (m) Time taken, t (s)

Average speed = Total distance traveled, s (m) Time taken, t (s)

*SPEED AND AVERAGE SPEED

VELOCITY*

Velocity is the speed in a given direction. It is defined as the rate of change of displacement.

The average velocity of a body is calculated by:

Average velocity = Total displacement, s (m) Time taken, t (s)

Both speed and velocity have the same SI unit. They are measured in meter per second or m s-1.

Speed is a scalar quantity and it has magnitude but no direction whereas velocity is vector quantity which has both magnitude and direction.

EXERCISE 2The world record for the 100 meter events was broken by Maurice Greene in 1999. His record time was 9.79 s. What was the average speed for the race?

A car starts from rest and accelerates uniformly at 3 ms-1. Calculatea) its velocity after 4 sb) its displacement after 6 s3.Diagram shows the graph of movement of an object

a) What is initial velocity of the object?b) What is the total distance of the movement of the object?c) What is the average velocity of the object?*

ACCELERATION AND DECELERATIONAcceleration is defined as the rate of change of velocity

It can be written as:

Acceleration = Change of velocity Time taken

= Final velocity (v) Initial velocity (u) Time takenor, a = v u tWhen the velocity of an object changes with time, an object is said to be accelerating.

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ACCELERATION AND DECELERATIONAcceleration is a vector quantity. The SI unit for acceleration is meter second per second or ms-2

The acceleration is positive if the velocity increases with time. The acceleration is negative if the velocity decreases with time.

Negative acceleration is also called deceleration or retardation.

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EXERCISE 3Figure shows the path traveled by a cyclist. He started his journey from O, moved a distance of 150 m to East towards A and then moved a distance 200 m to North towards B. The cyclist took about 25 s to complete his journeyDetermine(a) the total distance traveled(b) the displacement from O(c) the average speed of the cyclist(d) the average velocity of the cyclist

2.A lorry is moving in a straight road at a velocity of 10 ms-1. It then speeds up uniformly to a velocity of 30 ms-1 in 4 s. Immediately after this, the brake is applied and the lorry slows down uniformly and stops in the next. Calculate the acceleration of the lorry in the first 4 s and the last 5s.*

EQUATION OF LINEAR MOTIONThe equations used in linear motion involve two kinds of motion:Motion with constant velocity (zero acceleration)Constant change in velocity (constant acceleration)

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*EQUATIONS OF LINEAR MOTION The summary of equations is given below

Motion with constant velocityMotion with constant accelerationvav = s tvav = u + v 2s = vav x tS = ( u + v ) x t 2v = u + atS = ut + at2v2 = u2 + 2as

EXERCISE 4A car starts from rest at time t = 0 s and moves along a straight road. The figure below shows velocity-time graph of the car from t = 0 to 200 s?(a) Describe the motion of the car from t = 0 to 200 s.(b) Find the acceleration of the car inI) the first 20 sii) the last 10 s(c) Find the distance traveled by the car when the car isi) acceleratingii) moving with constant velocityiii) decelerating

2.The velocity-time graph of the motion is shown in below figure. Give an explanation for each line P, Q and R.Calculate the acceleration for the first 2 s?Calculate the total displacement of an object.

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*Displacement-Time Graph

Velocity-Time Graph* Acceleration = gradient of the graph Displacement = area under the graph

EXERCISE 5*1.Figure 3.1 shows a displacement-time graph for a moving object.What is the displacement of the object after

3 seconds?What is the velocity of the object during

i) the first 3 secondsii) the next 3 seconds?Plot the velocity-time graph for the object

The velocity-time graph for a car traveling along

a straight line is shown in figure 3.2.What is the acceleration of the car during the

part of the journey represented byi) OAii) ABiii) BCb) What is the total distance traveled by the car?c) Calculate the average velocity of the car for its whole journey?d) Plot the acceleration-time graph for the whole journey covered by the car

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