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Foundation year

Lecture 3:Velocity and Acceleration

General PhysicsPHYS 101

Instructor: Sujood Alazzam

2015/2016

CHAPTER OUTLINE

• Motion.• Vectors.• Velocity and Acceleration.• Force and Newton’s law of motion.• Hook’s Law.• Simple Pendulum.• Work ,Energy and Power.

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Velocity and Acceleration

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1.5 Average Speed and Average Velocity

• Average speed = distance /time taken.

• Average velocity = displacement/time taken

so average velocity is a vector! It can be negative.

Formula for average velocity:

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Example 1.5

At t1= 5 s, a car is at x1 = 600 m, and at t2=15 it

is at X2 = 500 m. Find its average velocity?

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2 1

500 60010 /

15 5

x xv m s

t t

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Example 1.6:

The position of a pinewood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of the car for (a) the first second, (b) the last 3 s, and (c) the entire period of observation.

t(s) 0 1.0 2.0 3.0 4.0 5.0

X(m) 0 2.3 9.2 20.7 36.8 57.5

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) 2.3 /

57.5 9.2) 16.1 /

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57.5 0) 11.5 /

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a v m s

x m mb v m s

t s

x m mc v m s

t s

Solu.

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Instantaneous Velocity

• That’s the velocity at one moment of time: car speedometer gives instantaneous speed.

• To find this, need to find car’s displacement in a very short time interval (to minimize speed variation).

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Cont.

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Mathematically, we write:

This “lim” just means taking a succession of shorter and shorter time intervals at the moment in time.

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1.6 Acceleration

Average acceleration = velocity change/time taken

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Cont.

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• Notice that acceleration relates to change in velocity exactly as velocity relates to change in displacement.

• Velocity is a vector, so acceleration is a vector.

Acceleration ( changes in v)

acceleration =change in velocity

elapsed time

a =change in velapsed time 13

Example 1.7

A car accelerates from rest to 30 m/s1 in 10 s. What is its average acceleration?

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2 1

30 03 /

10 0

v va m s

t t

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Instantaneous Acceleration

This is just like the definition of instantaneous velocity:

The instantaneous acceleration

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Constant Acceleration

Constant acceleration means the rate of change of velocity is constant.

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v changes object under acceleration

Average accelerationv

at

Instantaneous acceleration 0limt

va

t

d v

d t

2/a m s

Speeds up

Slows down

Cont.

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Example 1.8:

A particle moves according to the equation (x =10 t2 + 4 t – 6) where x is in meters and t is in seconds.

(a) Find the average velocity for the time interval from 1.00 s to 3.00 s.

(b) Find the instantaneous velocity at t = 0 s.

(c) Find the instantaneous acceleration at t = 1s.

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2

2

2

0

22

2 1

x 10 t   4 t – 6

( 3) 10(3) 4(3) 6 96

( 1) 10(1) 4(1) 6 8

96 8( ) 44 /

3 1

( ) 10 (2) 4 4 /

( ) 10 (2) 20 /

inst t

inst t

x t m

x t m

xa v m s

tx

b v t m st

xc a m s

t

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1.7 Our Units for One-Dimensional Motion

• Displacement: meters (can be positive or negative)

• Velocity= rate of change of displacement, units: Meters per second, written m/s.

• Acceleration= rate of change of velocity, units: Meters per second per second, written m/s2.

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System Time unit Length unit Mass unit

SI Units 1 second 1 m. the kilogram

CGS system 1 second 1 cm gram

F.P.S (the British system)

1 second 1 foot the pound

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Useful Approximations

• 1 foot ≈ 33 cm• 5 miles ≈ 8 kilometers.• 1 inch= 2.5 cm.• 1 Kg= 2.2 pound

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