C H A P T E R 3

ACCELERATION AND FREE FALL

ACCELERATION

• The changing of an object’s velocity over time.

• Average Acceleration

• SI Unit: m/s2

• Vector Quantity

ACCELERATION

• When velocity and acceleration are in the same direction, the speed of the object increases with time.

• When velocity and acceleration are in opposite directions, the speed of the object decreases with time.

ACCELERATION

• The camel is not slowing down, it’s velocity is increasing in the negative-x direction.

4.0s

vf=-10.0m/s

vi=-2.0m/s

ACCELERATION

• The camel is slowing down, it’s velocity and acceleration are in opposite directions.

4.0s

vi=-10.0m/s

vf=-2.0m/s

DECELERATION VS. NEGATIVE ACCELERATION

• Deceleration – Reduction in speed

• Negative Acceleration – Acceleration vector is in the negative-x direction

INSTANTANEOUS ACCELERATION

• The limit of the average acceleration as the time interval ∆t approaches zero.

MOTION DIAGRAMS

ONE-DIMENSIONAL MOTION WITH CONSTANT ACCELERATION

• Many applications of mechanics involve objects moving with constant acceleration

• Constant Acceleration• Instantaneous acceleration = average acceleration

COMPARING MOTION GRAPHS

VELOCITY AS A FUNCTION OF TIME

• where:

REALITY CHECK

• A sports car moving at constant speed travels 110m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in Express the answer in terms of “g’s,” where

• The initial velocity of the car is the average speed of the car before it accelerates.

• The final speed is 0 and the time to stop is 4.0 s.

DISPLACEMENT AS A FUNCTION OF TIME

The area under the line on a velocity vs. time graph is equal to the displacement of the object.

AN AUTOMOBILE MANUFACTURER CLAIMS THAT ITS SUPER-DELUXE SPORTS CAR WILL ACCELERATE UNIFORMLY FROM

REST TO A SPEED OF 38.9M/S IN 8.00S.

• a. Determine the acceleration of the car.

• b. Find the displacement of the car in the first 8.00s.

VELOCITY AS A FUNCTION OF DISPLACEMENT

EQUATIONS FOR MOTION IN A STRAIGHT LINE UNDER CONSTANT ACCELERATION

EquationInformation Given by Equation

Velocity as a function of time

Displacement as a function of time

Velocity as a function of displacement

IN COMING TO A STOP, A CAR LEAVES SKID MARKS 92.0M LONG ON THE HIGHWAY. ASSUMING A DECELERATION OF

7.00M/S2, ESTIMATE THE SPEED OF THE CAR JUST BEFORE BRAKING.

•

FREE FALL

• When air resistance is ignored, all objects in free fall near the Earth’s surface fall at the same constant acceleration.

• Galileo• Dropped objects of different weights of Leaning Tower of Pisa• Or did he?

• Inclined Planes• Diluting Gravity

FREE FALL

• Any object moving under the influence of gravity alone• Does not need to start from rest

• An object thrown up into the air is in free fall even when its altitude is increasing.

• Free Fall Acceleration (g)• Varies slightly with latitude• Decreases as altitude increases

• “Up” =positive direction

FREE FALL

• A tennis player on serve tosses a ball straight up. While the ball is in free fall , does the acceleration

• A. Increase• B. Decrease• C. Increase then Decrease• D. Decrease then Increase• E. Remain Constant

FREE FALL

• A tennis player on serve tosses a ball straight up. While the ball is in free fall , does the acceleration

• A. Increase• B. Decrease• C. Increase then Decrease• D. Decrease then Increase• E. Remain Constant

FREE FALL

• As the tennis ball in the previous question travels through the air, its speed

• A. Increases• B. Decreases• C. Decreases then Increases• D. Increases then Decreases• E. Remains the Same

FREE FALL

• As the tennis ball in the previous question travels through the air, its speed

• A. Increases• B. Decreases• C. Decreases then Increases• D. Increases then Decreases• E. Remains the Same

A BASEBALL IS HIT NEARLY STRAIGHT UP INTO THE AIR WITH A SPEED OF 22M/S.

• a. How high does it go?

• where,

• b. How long is it in the air?