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PPMF101 – Lecture 4PPMF101 – Lecture 4

Motions in 1 & 2 DimensionsMotions in 1 & 2 Dimensions

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Vector & Scalar quantityVector & Scalar quantityVectorVector

A quantity that has A quantity that has magnitude and magnitude and direction.direction.

Eg. Displacement,Eg. Displacement,

velocity, acceleration, velocity, acceleration, force, momentum, force, momentum, impulse, weight, impulse, weight, friction, tension, friction, tension, electric and magnetic electric and magnetic field. field.

ScalarScalar

A quantity that has A quantity that has magnitude only.magnitude only.

Eg. Distance, speed, Eg. Distance, speed, pressure, energy, pressure, energy, heat, work, power, heat, work, power, time, charge and time, charge and temperature.temperature.

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Distance & DisplacementDistance & DisplacementDistanceDistance

Scalar quantityScalar quantity

Magnitude only Magnitude only

DisplacementDisplacement

Vector quantityVector quantity

Magnitude and Magnitude and directiondirection

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Speed Speed Speed refers to how far an object Speed refers to how far an object travels in a given time interval, travels in a given time interval, regardless of direction.regardless of direction.

A scalar quantity.A scalar quantity.

totaldis tan ceaverage speed

total time

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velocityvelocity

Velocity is used to signify both the Velocity is used to signify both the magnitude (numerical value) of how magnitude (numerical value) of how fast an object is moving and the fast an object is moving and the direction in which it is moving.direction in which it is moving.

A vector quantity.A vector quantity.

total displacementaverage velocity

total time

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Instantaneous velocity Instantaneous velocity Instanteneous Instanteneous velocity at any velocity at any moment is moment is defined as the defined as the average velocity average velocity over an over an infinitesimally infinitesimally short time short time interval.interval.

t

xlimvt

0

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AccelerationAccelerationAcceleration specifies how rapidly the Acceleration specifies how rapidly the velocity of an object is changing.velocity of an object is changing.If velocity is increasing it is called If velocity is increasing it is called acceleration.acceleration.If velocity is decreasing it is called If velocity is decreasing it is called negative acceleration or negative acceleration or decelerationdeceleration..

elapsedtime

velocityofchangeonacceleratiaverage

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Instantaneous accelerationInstantaneous acceleration

dt

dv

t

vlimat

0

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Graph: displacement (s) vs time (t)Graph: displacement (s) vs time (t)

Slope = velocitySlope = velocity

s

t

s

t

constant velocity

zero velocity

Graph: displacement (s) vs time (t)Graph: displacement (s) vs time (t)

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s

t

increasing velocity

s

t

decreasing velocity

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Graph: velocity(v) vs time(t) (p.25)Graph: velocity(v) vs time(t) (p.25)

Slope = accelerationSlope = acceleration

Area under the graph Area under the graph = distance travelled= distance travelled

v

t

velocity increasing uniformly & constant acceleration

v

t

constant velocity & zero acceleration

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Graph: acceleration(a) vs time(t)Graph: acceleration(a) vs time(t)

For constant For constant acceleration.acceleration.

The graph is a The graph is a straight horizontal straight horizontal line.line.

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v vs t & s vs t graphs: braking v vs t & s vs t graphs: braking distancesdistances

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S vs t & v vs t graphs: catching a S vs t & v vs t graphs: catching a speeder (p.31)speeder (p.31)

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Equations of motionEquations of motion

Constant Constant acceleration aacceleration a

Constant Constant acceleration due to acceleration due to gravity ggravity g

tvus

asuv

atuts

atuv

2

1

2

2

1

22

2

tvus

gsuv

gtuts

gtuv

2

1

2

2

1

22

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ExamplesExamples

1. A runner leaves the starting blocks 1. A runner leaves the starting blocks and accelerates at 2.50 m/s2 for 4.00 and accelerates at 2.50 m/s2 for 4.00 s. What speed does the runner reach?s. What speed does the runner reach?

2. An airplane that is flying level needs to 2. An airplane that is flying level needs to accelerate from a speed of 200 m/s to a accelerate from a speed of 200 m/s to a speed of 240 m/s while it flies a speed of 240 m/s while it flies a distance of 1200 m. What must the distance of 1200 m. What must the acceleration of the plane be?acceleration of the plane be?

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3. A rock is dropped from a vertical 3. A rock is dropped from a vertical cliff. The rock takes 7.00 s to reach cliff. The rock takes 7.00 s to reach the ground below the cliff. What is the ground below the cliff. What is the height of the cliff?the height of the cliff?

4. If an object was freely falling, from 4. If an object was freely falling, from what height would it need to be what height would it need to be dropped to reach a speed of 70.0 dropped to reach a speed of 70.0 m/s before reaching the ground?m/s before reaching the ground?

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Eg. 1Eg. 1Determine the average velocity forDetermine the average velocity for(i) the first 3 seconds(i) the first 3 seconds(ii) the entire motion(ii) the entire motion

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Eg. 2Eg. 2This is a graph for a moving object.This is a graph for a moving object.

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Eg. 2 continueEg. 2 continue

(i) Explain the motion at PQ and RS.(i) Explain the motion at PQ and RS.

(ii) What is the total displacement of (ii) What is the total displacement of the object? the object?

(iii) What is the time for the motion (iii) What is the time for the motion of the object?of the object?

(iv) Determine its average velocity.(iv) Determine its average velocity.

(v) What is its acceleration at (v) What is its acceleration at

t = 22 s?t = 22 s?

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Eg. 3Eg. 3A car is driven from point O at the A car is driven from point O at the north with velocity 60 km/h for 10 min north with velocity 60 km/h for 10 min until it reached a junction, S. The car until it reached a junction, S. The car then turn west and moved with a then turn west and moved with a velocity of 30 km/h for another 10 min velocity of 30 km/h for another 10 min until its reached point A. Determineuntil its reached point A. Determine(a) the average speed of the car from O (a) the average speed of the car from O to A.to A.(b) the average velocity of the car from (b) the average velocity of the car from O to A. O to A.

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Eg. 4Eg. 4

A mouse deer runs a distance of 70 m A mouse deer runs a distance of 70 m between two points at a constant between two points at a constant acceleration in 7.0 s. Its velocity while acceleration in 7.0 s. Its velocity while passing through the second point is 15.0 passing through the second point is 15.0 m/s.m/s.

(a) What is its speed at the first point?(a) What is its speed at the first point?

(b) What is the acceleration of the mouse (b) What is the acceleration of the mouse deer?deer?

Projectile Motion

A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

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Projectile Motion

If an object is launched at an initial angle of θ0 with the horizontal, the analysis is similar if θ0 = 0 launched from certain height, except that the initial velocity has a vertical component.

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It can be understood by analyzing the horizontal and vertical motions separately.

Projectile Motion

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Projectile Motion

The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration g.

This photograph shows two balls that start to fall at the same time. The one on the right has an initial speed in the x-direction. It can be seen that vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly.

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Projectile MotionProjectile Motion

ProjectileProjectile motion is motion with motion is motion with constant acceleration in two constant acceleration in two dimensions, where the acceleration dimensions, where the acceleration is is gg and is downward. and is downward.

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Solving Problems Involving Solving Problems Involving Projectile MotionProjectile Motion

Example 3-6: Driving off a cliff.

A movie stunt driver on a motorcycle speeds horizontally off a 50.0-m-high cliff. How fast must the motorcycle leave the cliff top to land on level ground below, 90.0 m from the base of the cliff where the cameras are? Ignore air resistance.

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Projectile MotionProjectile MotionExamples of projectile motion. Notice the effects of air resistance.

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Water fountain fireworks

metal grinding