BB101 Chapter 2 Linear Motion.edit (1)

LINEAR MOTION BB101- ENGINEERING SCIENCE

UNIT SAINS JMSK PUO/JUN 2012 Page 10

2.0 LINEAR MOTION

2.1 Scalar and Vector Quantity A scalar quantity is a quantity that has magnitude, but no direction. A vector quantity is a quantity that has both magnitude and direction. Table shows examples of scalar and vector quantities.

Scalar quantity Vector quantity

Distance Displacement

Area Acceleration

Speed Force

2.2 Linear Motion Linear motion is motion in a straight line. Example of linear motion are: a) A car moving in a traight line. b) A passenger carried by the moving escalator. Example of non-linear motion are: a) A snake crawling. b) A top spinning.

2.3 Uniform and non–uniform motion

Uniform motion : a constant steady speed or motion. On a graph it appears as a straight line going neither up nor down. Motion moving in a straight line at a constant speed. Non–uniform motion : Most of the motion that we come across in daily life is non-uniform

motion. Moving objects are either 'speeding up' or 'slowing down'. In non-uniform motion,

the velocity of the moving object changes, as a result of which the object is said to have an

acceleration.

2.4 Distance and Displacement

Distance travelled by an object is the total length that is travelled by that object. Distance is a scalar quantity. The SI unit of distance is m (metre).

Displacement of an object from a point of reference, O is the shortest distance of the object from point O in a specific direction. Displacement is a vector quantity. The SI unit of displacement is m (metre).

http://en.wikipedia.org/wiki/Motion_(physics)



Distance vs Displacement

Distance travelled = 200m

Displacement = 120 m, in the direction of Northeast

Comparison between distance and displacement

Aspect Distance Displacement

Definition Total route taken by a motion

Distance taken with consideration of direction

Type of quantity

Scalar quantity-with magnitude only

Vector quantity-direction and magnitude are important

SI unit Metre (m)

2.5 Speed and Velocity

Speed is a scalar quantity which refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. An object with no movement at all has a zero speed. Speed = distance travelled/time taken Velocity is a vector quantity which refers to "the rate at which an object changes its position." Velocity = displacement/time Comparison between speed and velocity

Aspect Speed Velocity

Definition Rate of change of distance Rate of change of displacement

Type of quantity

Scalar quantity-with magnitude only

Vector quantity-direction and magnitude are important

Formula

SI unit ms-1

2.6 Average velocity & Instantaneous velocity

Velocity shows how fast an object is moving to which direction.

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/forceandmotion/images/LinearMotion.png



Average velocity can be calculated by dividing displacement over time.

For example, when a car moved 50 km in 2 hours, the average velocity is 25.5 km/h because

The instantaneous velocity shows the velocity of an object at one point.

For example, when you are driving a car and its speedometer swings to 90 km/h, then the instantaneous velocity of the car is 90 km/h.

2.7 Acceleration and deceleration

a) An object accelerates when its velocity changes with time. Acceleration is defined as the rate of change of velocity with time.

b) The acceleration of an object is regarded as positive if its velocity increases and

negative if its velocity decreases. Negative acceleration is also known as deceleration.

c) An object is said to move with uniform acceleration if the rate of change of its velocity is constant.

d) An object is said to move with zero acceleration if its velocity remains constant.

Examples

a) A car increases its velocity steadily from 72 km h-1 to 108 km h-1 in 5 s. What is its acceleration in m s-2? Solution ,

, , ,

b) An object moves from rest with a uniform acceleration of 2 m s-2. What is the velocity of the object after 30 s? Solution ,

, , ,

,

c) A car moving at constant velocity of 30 cm s-1 came to a stop 6 s after its brake was applied. What was the deceleration of the car? Solution , , , ,

,

2.8 Equations of Linear Motion

Problems on linear motion with uniform acceleration can often be solved quickly using the equations of motion. The following symbols are used in the equations of motion.



, , , ,

There are four equations of linear motion, that are:

,

,

,

Examples

a) A car is accelerated at 6 m s-2 from an initial velocity of 2 m s-1 for 10 seconds. What is the final velocity, and the distance moved?

Solution

b) A driver travelling at a velocity of 108 km h-1 notices a cow in the middle of the road 80 m in front of him. On seeing the cow. The driver instantly applies the brakes and is able to bring the car to a stop after 6 seconds.

i. What is the deceleration of the car? ii. Calculate the distance travelled by the car from the time the driver applies

the brakes until it comes to a stop. iii. Is the driver able to avoid knocking the cow?

Solution



, ,

c) A ball is thrown vertically upwards with an initial velocity of 15 m s-1. Neglecting air resistance, find

i. The maximum height reached, ii. The time taken before it reaches the ground.

(Acceleration due to gravity = 10 m s-2)

Solution

, , ,

, ,

2.9 Analysing Motion Graphs

Velocity – Time Graph

A velocity – time graph shows how the velocity of an object changes with time.

The gradient of a velocity – time graph represents the acceleration of the object.

The area under a velocity – time graph represents the distance travelled by the object.



Solving Problems using Graphs which show linear motion Example: A car moving at a velocity of 30 ms-1 accelerates constantly and reaches a velocity of 35 ms-1 in 6 seconds. The car moves with a velocity of 35 ms-1 for 30 seconds. The car then stops for 4 seconds. Calculate: (a) the acceleration for the first 6 seconds. (b) the deceleration for the last 4 seconds. (c) the total distance travelled (a) Given :

=

(b) Given:

a =

=

Velocity/ms-1

Time/s

6

m

e

/

s

36 40

30

35

me

/s

A B

C



(c) Total distance = Area below the graph = Area A + Area B + Area C

=

(35

= 195 + 1 050 + 70 = 1 315 m Study of Motion with the Ticker Timer:



2.10 Exercises 1.Give the definition and unit for each of the following.

a)Displacement b)Distance c)Velocity d)Speed e)Acceleration

2. State the difference between :

a) distance and displacement b) speed and velocity

c) acceleration and deceleration d) Scalar quantities and vector quantities

3. A car moves in a straight line from its stationary state with a uniform acceleration. It

achieves a velocity of 120 m/s after moving through a distance of 500m. Calculate ,

i. The acceleration of the car

ii. The time taken

iii. The velocity when t=3 s

4. A car moving at a velocity of 20m/s accelerates constanly and reaches a velocity of

30m/s in 10 seconds. The car moves with a velocity of 30m/s for 30 seconds. The car

then stops for 5 seconds. Calculate,

i. The acceleration for the first 10 seconds

ii. The deceleration for the last 5 seconds

iii. The total distance travelled

5. A ball is thrown vertically upwards with an initial velocity of 20m/s . Calculate

i. The maximum height of the ball

ii. The total time the ball is in the air, ( take g = 9.81 m/s2 )

iii. The time to reach a height of 15 m

iv. The velocity when the ball is at height of 15m.

6. Figure shows a velocity – time graph for a moving object

i. State the meaning of each lines P, Q, and R.

ii. What is the acceleration of the objects in the first 2 seconds?

iii. What is the total distance of the object?

7. A car starts from rest and accelerates at a constant acceleration of 2m/s2 for 5 s.

The car then travels at a constant velocity for 9 s . The brakes are then applied and the

car stops in 6 s. What is the maximum velocity attained by the car?

(i) Plot a velocity-time graph for the whole journey.

(ii) From the graph-plotted, determine the total distance travelled.

Answer: 3. i. 14.4m/s2 ii. 8.3 s iii. 43.2m/s 4. i. 1m/s2 ii. -6m/s2 iii. 415m 5. i. 20.4 m ii. 4.08s iii. 0.99s iv. 10.29m/s 6. ii. 2.5 m/s iii. 45m 7. 10m/s (ii) 145m

Minimum requirement assessment task for this topic:

1 Theory Test & 1 Lab work Specification of Theory Test : CLO1 - C1 & CLO3 – (C2, A1)



Specification of lab work: CLO2 - (C2,P1) *****************************************************************************************

COURSE LEARNING OUTCOME (CLO)

Upon completion of this topic, students should be able to:

1. Identify the basic concept of linear motion, (C1)

2. Apply concept of linear motion to prove related physics principles. (C2,P1)

3. Apply the concept of linear motionin real basic engineering problems. (C2,A1)

Compliance to PLO : PLO1 , LD1 (Knowledge) – Test 1 PLO2, LD2 (Practical Skill) – Experiment 2 PLO4, LD4 (Critical Thinking and Problem Solving Skills) – Test 1

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BB101 Chapter 2 Linear Motion.edit (1)