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