2.1c Acceleration
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Acceleration = rate of change in velocity
Acceleration = change in velocity time a = acceleration vf = final velocity vi = initial velocity
a =
Vf - Vi t
• Acceleration- has direction, just like velocity. • Acceleration is a VECTOR (it has both a magnitude and a direction).
• The roller coaster accelerates both because its speed changes and its direction
For its velocity to change, an object must accelerate. An object accelerates whenever its speed or direction or both change. So this means….
An object moving in a circle at constant speed is always accelerating (changing direction).
Acceleration at constant speed How can you accelerate at a constant speed?
It’s like gravity. An object’s velocity gets faster every second, but it gets faster at the same rate. Objects accelerate toward the earth at a rate of 9.8 m/s2. In other words they fall 9.8m/s faster every second.
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
distance traveled in the first second
1 .3 m
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
distance traveled in the second second.
1 .3 m
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
distance traveled in the third second
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
distance traveled in the fourth second
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
0.4 , 0.7 , 1.0 , 1.3 is an arithmetic progression with a common difference 0.3. This is an important characteristic of motion with uniform acceleration.
ACCELERATION
Acceleration is the change in speed in an object in a period of time. change in Where do the units come from? Δv velocity (m/s) a=v÷t acceleration a = m/s ÷ s a Δt (m/s/s) a = m/s/s change in time (s)
=m/s2 It takes a cyclist 20 seconds to go from a standing start to 14m/s. What is their acceleration?
a = Δv/Δt a = 14m/s / 20s
What is 14m/s in km/hr?
= 14 × 60s × 60min ÷ 1000m
a = 0.7ms-2
= 50.4km/hr
Acceleration
ΔV
Acceleration = change in velocity (in m/s) (in m/s2)
time taken (in s)
A
T
•
A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration?
•
A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by?
•
A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take?
•
A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?
SPEED/TIME GRAPHS Using the speed/time graph: 3. What distance is covered in part 1? d=v×t d = 4m/s × 10s d = 40 m
Speed
8
(m/s)
4. What is the total distance covered?
4
Part 1 = 40m 10
Part 2 = 0m Part 3 = 0m Part 5 = v × t
= 8m/s × 10 s
= 80m
Part 4 = v × t ×
= 8m/s × 5s ×
= 20m
Total
= 40 + 80 + 20
=140m
20 Time (sec)
30
ACCELERATION QUESTIONS What would these look like on a speed/time graph? 1. stopped
2. slow
3. fast
4. accelerating
Velocity-time graphs
1) Upwards line =
4) Downward line = constant accel opposite direction
Constant 80 acceleration Velocity m/s
60 40 20 0
10
2) Horizontal line = Constant velocity
20
30 40 50 3) Upwards line = constant accel, slower velocity
T/s
80
Velocity m/s
60 40 20 T/s
0
10
20
30
40
1) How fast was the object going after 10 seconds? 2) What is the acceleration from 20 to 30 seconds? 3) What was the deceleration from 30 to 50s? 4) How far did the object travel altogether?
50
Which car (red, green, or blue) experiences the greatest acceleration? Blue car has the greatest acceleration
Match the car to the graph
Match the car to the appropriate graph line.
MORE RESOURCES • • • •
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/C http://www.fearofphysics.com/Xva/xva.html http://www.quia.com/rr/121411.html?AP_rand= http://www.physics4kids.com/files/motion_veloc
Acceleration = change in velocity time a = acceleration vf = final velocity vi = initial velocity
a =
Vf - Vi t
• Acceleration- has direction, just like velocity. • Acceleration is a VECTOR (it has both a magnitude and a direction).
• The roller coaster accelerates both because its speed changes and its direction
For its velocity to change, an object must accelerate. An object accelerates whenever its speed or direction or both change. So this means….
An object moving in a circle at constant speed is always accelerating (changing direction).
Acceleration at constant speed How can you accelerate at a constant speed?
It’s like gravity. An object’s velocity gets faster every second, but it gets faster at the same rate. Objects accelerate toward the earth at a rate of 9.8 m/s2. In other words they fall 9.8m/s faster every second.
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
distance traveled in the first second
1 .3 m
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
distance traveled in the second second.
1 .3 m
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
distance traveled in the third second
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
distance traveled in the fourth second
An object is moving with uniform acceleration. Its positions at one-second interval are shown below. t = 0 s
t = 1 s
t = 2 s
t = 3 s
t = 4 s
O
p o s itiv e d ire c tio n 0 .4 m
0 .7 m
1 .0 m
1 .3 m
0.4 , 0.7 , 1.0 , 1.3 is an arithmetic progression with a common difference 0.3. This is an important characteristic of motion with uniform acceleration.
ACCELERATION
Acceleration is the change in speed in an object in a period of time. change in Where do the units come from? Δv velocity (m/s) a=v÷t acceleration a = m/s ÷ s a Δt (m/s/s) a = m/s/s change in time (s)
=m/s2 It takes a cyclist 20 seconds to go from a standing start to 14m/s. What is their acceleration?
a = Δv/Δt a = 14m/s / 20s
What is 14m/s in km/hr?
= 14 × 60s × 60min ÷ 1000m
a = 0.7ms-2
= 50.4km/hr
Acceleration
ΔV
Acceleration = change in velocity (in m/s) (in m/s2)
time taken (in s)
A
T
•
A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration?
•
A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by?
•
A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take?
•
A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?
SPEED/TIME GRAPHS Using the speed/time graph: 3. What distance is covered in part 1? d=v×t d = 4m/s × 10s d = 40 m
Speed
8
(m/s)
4. What is the total distance covered?
4
Part 1 = 40m 10
Part 2 = 0m Part 3 = 0m Part 5 = v × t
= 8m/s × 10 s
= 80m
Part 4 = v × t ×
= 8m/s × 5s ×
= 20m
Total
= 40 + 80 + 20
=140m
20 Time (sec)
30
ACCELERATION QUESTIONS What would these look like on a speed/time graph? 1. stopped
2. slow
3. fast
4. accelerating
Velocity-time graphs
1) Upwards line =
4) Downward line = constant accel opposite direction
Constant 80 acceleration Velocity m/s
60 40 20 0
10
2) Horizontal line = Constant velocity
20
30 40 50 3) Upwards line = constant accel, slower velocity
T/s
80
Velocity m/s
60 40 20 T/s
0
10
20
30
40
1) How fast was the object going after 10 seconds? 2) What is the acceleration from 20 to 30 seconds? 3) What was the deceleration from 30 to 50s? 4) How far did the object travel altogether?
50
Which car (red, green, or blue) experiences the greatest acceleration? Blue car has the greatest acceleration
Match the car to the graph
Match the car to the appropriate graph line.
MORE RESOURCES • • • •
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/C http://www.fearofphysics.com/Xva/xva.html http://www.quia.com/rr/121411.html?AP_rand= http://www.physics4kids.com/files/motion_veloc
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