Chapter 3Accelerated MotionAccelerated Motion

Acceleration Acceleration = change

in speed or velocity over time. It is the rate at which an object’s velocity changes.

It could be speeding up, slowing down, or changing directions

Acceleration Acceleration = change in speed or

velocity over time. It is the rate at which an object’s velocity changes.

It could be speeding up, slowing down, or changing directions

Four possibilities Speeding up forward

Slowing down forward

Speeding up backwards

Slowing down backwards

Acceleration a = v = vf – vi

t tf – ti

Average acceleration = change in velocity during a time interval divided by the time interval

Acceleration a = v = vf – vi

t tf – ti Average acceleration = change in velocity

during a time interval divided by the time interval

Instantaneous acceleration = Drawing a tangent line on the velocity-time graph at the point of interest and calculate the slope

Accelerationa = v = vf – vi

t tf – ti

Velocity with avg. acceleration

v = a t vf – vi = a t

vf = Vi + a t

Accelerationa = v = vf – vi

t tf – ti

Velocity with avg. acceleration

v = a t vf – vi = a t

vf = Vi + a t

Accelerationa = v = vf – vi

t tf – ti

Velocity with avg. acceleration

v = a t vf – vi = a t

vf = Vi + a t

Acceleration

Acceleration

Acceleration

Acceleration

Acceleration

Position with Average Acceleration An object’s final position is

equal to the sum of its initial position, the product of the initial velocity and the final time, and half the product of the acceleration and the square of the final time

xf = xi + vitf + ½ a tf2

Velocity with constant Acceleration The square of the final velocity

equals the sum of the square of the initial velocity and twice the product of the acceleration and the displacement since the initial time

vf 2 = vi

2 + 2a(xf - xi)

Free Fall Free Fall – The motion

of an object when gravity is the only significant force acting on it

Acceleration due to gravity = 9.8 m/s2 =

32 ft/s2 = 22 mph/s Can be + or -

Free Fall Free Fall – The motion

of an object when gravity is the only significant force acting on it

Acceleration due to gravity = 9.8 m/s2 =

32 ft/s2 = 22 mph/s Can be + or -

Free Fall

2nd Law of Motion Falling objects – All

objects fall at the same rate

Large mass small mass

Big Forcelittle acceleration

Little force

big acceleration

Free Fall rides

Calculating velocity

vf = Vi + a t Vi = 0.0 m/s Acceleration due to

gravity = 9.8 m/s2

Can be + or -

Free Fall rides

vf = Vi + a t Vi = 0.0 m/s Acceleration due to

gravity = 9.8 m/s2

Can be + or -

Free Fall rides Calculating

distance falling

xf = xi+vitf+ ½ a tf2

xi = 0.0 m Vi = 0.0 m/s Acceleration due to gravity = 9.8

m/s2

Can be + or -

2nd Law of Motion

Falling objects – All objects fall at the same rate

Large mass small mass

Big Forcelittle acceleration

Little force

big acceleration

2nd Law of Motion

Falling objects – All objects fall at the same rate

Large mass small mass

Big Forcelittle acceleration

Little force

big acceleration

Free Fall Variations: Acceleration due to

gravity = 9.8 m/s2 on earth’s surface

Depends on mass of object (planet) and distance from center