Lecture: Acceleration A vector quantity CCHS Physics.
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Transcript of Lecture: Acceleration A vector quantity CCHS Physics.
Lecture: Acceleration A vector quantity
CCHS Physics
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Acceleration• The rate of change in velocity
• We can change the velocity of an object by:
– changing its speed– changing its direction– (or changing both)
aavg =ΔvΔt
Meaning of Acceleration• In everyday language ‘acceleration’ refers to
a gain in speed and ‘deceleration’ to a decrease in speed.
• In physics we will speak only of acceleration, and we will define it as being either positive or negative.
• Acceleration is positive when the change in velocity is positive and negative when the change in velocity is negative.
True or false?• If your speed is increasing, you must have a
positive acceleration.
ANSWER
False! • To increase speed in positive direction
= positive accelerationbut an increase in speed in the negative direction = negative acceleration
Acceleration Video
Reminders
• Velocity is the rate of change of position. It can be found graphically by taking the slope of a position vs. time graph.
• Acceleration is the rate of change of velocity. It can be found graphically by taking the slope of a velocity vs. time graph.
Let’s try some examples…• A car starts from rest and accelerates
uniformly at 3 m/s2 north. What is its velocity after 5 seconds?
• A bus traveling west at 20 m/s slows uniformly to 8 m/s in 6 seconds. What is its acceleration?
a =vf −v1
t 3=
vf −05
vf =15 m/s north
a =vf −v1
t a=
20 −86
a=−2 m/s2 =2 m/s2 east
Acceleration Graphing Movie
Try this one…
• During which of the following intervals is the acceleration the greatest: t = 0 - 3 st = 3 - 6.2 st = 6.2 - 9 s
• Ha ha that was a trick. It’s zero everywhere.
• How would a position vs. time graph look like if an object was accelerating?
Let’s Add in Some Calc!• Instantaneous Acceleration
• Relating back to position:
• So, acceleration is the second derivative of position with respect to time
a =dvdt
a =dvdt
=ddt
dxdt
⎛⎝⎜
⎞⎠⎟=
d2xdt2
Calc Example• If the velocity of dog is given by the
equation v(t) = 5t + 1, what is the acceleration of the dog at 4 s?
• If the position of a bee is given by the equation x(t) = .6t2 + 3t + 1, what is the acceleration of the snail at 7 s?
a =dvdt
=ddx
5t+1( ) = 5 m/s2
v =dxdt
=ddx
.6t2 + 3t+1( ) =1.2t+ 3
a =dvdt
=ddx
1.2t+ 3( ) =1.2 m/s2
QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
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“What about Integrals?” - Integral Man
• So, remember that derivatives and integrals and opposites:
• EXAMPLE: If the acceleration of a bus is given by a(t) = 2t, what is the velocity after 4 s if the initial velocity is 7 m/s?
– We’ve got to solve for C using initial conditions
v = a( )dt∫ x = a( )dt∫∫
v = adt=∫ 2tdt0
4
∫ =t2 +C
v 0( ) =7 ⇒ 7 =02 +C ⇒ C =7 m/sv t( ) =t2 + 7
v 4( ) =42 + 7 = 23 m/s