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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?
22 1
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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