ACCELERATION
Chapter 4
Acceleration
• A change in velocity (speed or direction)
Average Acceleration• How fast the velocity changes• For example: 5 miles/hour/second 5 miles per hour per second
Units• Meters per second per second: m/s/s• Or Meters per second squared
Negative Acceleration
• Acceleration (not motion) in the backward direction
• Results in “deceleration” (slowing down)
Acceleration Graphs• Constant Acceleration • Straight Line • Changing Acceleration
• Curved line
Calculating Velocity (final) of an object with constant acceleration
v = at
4.2 DISPLACEMENT DURING CONSTANT ACCELERATION
Average Velocity• With constant acceleration
Displacement when velocity and time are Known• A car is traveling at 20 m/s and accelerates at a constant rate to 40 m/s in
5 seconds. What is its average velocity? How far did the car travel?
d = ½ (vf + vi)t
d = vt_
Rearrange to solve for displacement
The equation below is a combination of the two equations
Equation for average velocity
Displacement when original velocity, acceleration and time are known
Combining these two equations (substitute Vf from second equation into the first equation
d = ½(vf + vi)t Vf = Vi + at
Yields this equation
Displacement when original velocity, acceleration and time are known
• A car accelerates from rest at a rate of 6.1 m/s/s for 7.0 s. How far does the car move?
Displacement when acceleration and velocity are known
Combine the equations for final velocity and displacement
d = ½ (vf + vi)t vf = vi + at
Solving for Vf yields this equation
Calculating Acceleration From Displacement and Velocity
• An airplane must reach a velocity of 71 m/s for takeoff. If the runway is 1.0 km long, what must the acceleration be?
Rearrange the equation to solve for x
The plane lands going 71 m/s. It slows to a halt with an acceleration of -2.5 m/s/s. How much runway does it require?
ACCELERATION DUE TO GRAVITY
Acceleration due to Gravity
• Galileo• All objects fall to
Earth with the same constant acceleration
Acceleration Due to Gravity• Downward direction is negative • -9.8 m/s/s
Acceleration Due to Gravity
Equations• All the same equations for constant acceleration• Just replace a with g
Distance Traveled
• An object falls for a given amount of time, how far does it fall?
Time• An object falls a given distance, how long will it take to hit the
ground?• Rearrange the equation to solve for t
Final Velocity• An object free falls for a given amount of time,
how fast is it going when it hits the ground?• Different than average velocity
Vf = Vi + gt
Example Problem 2• See page 78• What equation will
you use for part a?• Solve for x
• For part b, solve for time using• Vf = Vi + gt• Vf = 0
Read Problem Solving Strategy on Page 78
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