Constant Acceleration Date __________
Chapter 2: pages 51­ 64
When the velocity of an object changes the same amount each second, is it called constant acceleration. The best example of this is falling objects, but other moving objects can also have constant acceleration.
Galileo was interested in falling objects. At that time there weren't sensitive timing devices so he started with inclined plane experiments.
Galileo rolled balls down inclined planes.
As the ball rolls down the inclined plane, the _____________ of the ball will change the same amount each second which is
________________ ____________________.
1
Let's say that the velocity of the ball increases by 2 m/s every second as it rolls down the incline.
The ball would have an acceleration of ________.
Time (s)
Velocity (m/s)
Galileo saw that the velocity of the ball at any time was equal to the acceleration times time: v = aΔt
0
1 Time (s)
Acceleration x time = Velocity
2 0 2 m/s2 x 3 1 2 m/s2 x
4 2 2 m/s2 x
3 2 m/s2 x
4 2 m/s2 x
2
Galileo continued his inclined plane experiments with steeper and steeper inclines until there was a maximum acceleration when the ball was dropped vertically.
If air resistance is ignored, all objects dropped near the surface of the Earth will fall with the same constant acceleration.
The motion of free fall assumes: _____________________
The acceleration is only due to the force of _____________
The acceleration due to gravity, g, is 9.8 m/s2 is directed
downward. Since we have chosen that the downward
direction as negative, the acceleration of objects in
free fall near the surface of the Earth is ____________
3
During each second of free fall, the velocity of the object increases by 9.8 m/s.
The velocities are negative because downward is defined as negative.
Time (s)
Velocity (m/s) 0 1 2 3
4 5 For free fall, the velocity at any time is the acceleration due to gravity times the time or Why is the velocity negative?
4
Acceleration is constant during upward or downward motion.
This is a picture of a ball thrown up into the air with an initial velocity of 10.5 m/s.
On the left the ball is moving up. On the right the ball is falling down.
The graph shows the velocity of the ball versus time.
What does the slope of the line represent?
What is the value of the slope?
What is the velocity of the ball when it reaches the point that is was let go?
Assuming no air resistance, what is the only force acting on the ball?
5
The distance traveled by the ball can also be determined.
6
Remember g = ­9.8 m/s2
Time of fall (s) Velocity (m/s) 1/2g(Δt2) = Displacement (m) 0 0 m/s 1/2 (­9.8 m/s2) x
1 ­9.8 m/s 1/2 (­9.8 m/s2) x
2 ­19.6 m/s 1/2 (­9.8 m/s2) x
3 ­29.4 m/s
1/2 (­9.8 m/s2) x
4 ­39.2 m/s 1/2 (­9.8 m/s2) x
5
­49.0 m/s 1/2 (­9.8 m/s2) x
The displacement values are negative since we have chosen the downward direction as negative.
As the object falls it will fall through an ever increasing distance because the velocity is increasing.
7
All objects do not fall with an equal acceleration due to air resistance.
Heavy, round objects like stones and balls are not affected much by air resistance.
Feathers and flat objects are affected more by air resistance.
A good approximation for the motion of objects is
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