PHYSICS 103: Lecture 3

• Motion under uniform acceleration

• Freely falling objects Acceleration due to gravity Tracking a falling object

• Motion under uniform acceleration

• Freely falling objects Acceleration due to gravity Tracking a falling object

Agenda for Today:

Description of Motion with Uniform Accleration

Remember from last class that acceleration is:

t

v

timeelapsed

yin velocit change on accelerati Average

t

v- v

t

v a

0

v = final velocityv0 = initial velocity

Where:

at v v 0

If a is constant:

Example of Uniform Accleration:

A car accelerates at 3 m/s2 from rest. What is the final velocity after 20 seconds?

at v v 0

We know:

v0=0 m/s a=3 m/s2 t=20 s

m/s 60 s 20sm3 0 v 2

How far did it travel in this time?

Remember from last class that distance is:

t

d

travelof time

traveleddistance v velocity Average

t v d

2

vv v

o

at v v 0

If acceleration, a, is constant, then:

If acceleration, a, is constant, then the final velocity, v, is given by:

so: 20

00ta

2

1 t vt

2

atvvt v d

Motion with Uniform Acceleration

d = d0 + v0t + 1/2at2 d = d0 + v0t + 1/2at2

Initial distance at t = 0

acceleration

Initial velocity:

velocity at t = 0

v= vo + atv= vo + at

Initial velocity:

velocity at t = 0

acceleration

Final velocity

When an object accelerates at a constant rate the following applies:

Example Problems for Uniform Accleration:

4)A car starts out at a velocity of 2 m/s. If its acceleration is 3 m/s2, how long will it take the car to travel 640 m?

1) A car starts out at a velocity of 2 m/s. If it's acceleration is 3 m/s2, how fast will it be going in 20 s?

2) A car starts out at a velocity of 2 m/s. If it's acceleration is 3 m/s2, how long will it take before it will be going 62 m/s

3) In the problem above, how far will it have traveled?

Freely falling objects

1) Heavy objects and light objects fall at the same rate with no air resistance

2) Things fall faster and faster until they hit the ground (acceleration)

Observations:

Time Distance Velocity

0 0 0

0.05 s 1.2 cm 24 cm/s

0.10 s 4.8 cm 72 cm/s

0.15 s 11.0 cm 174 cm/s

g 9.8 t

v a 2s

m

Acceleration due to Gravity

Free-fall is an example of motion with uniform acceleration

A ball is dropped from a a tall building.How long does it take to reach the ground? How fast is it going?

initial

final

where h = 1224 ft = 373 m to 102nd floor

v= vo + at

d = d0 + v0t + 1/2at2

d=373 m d0=0 m v0=0 m/s

200 ta

2

1 t v d d

0 0

s 64.8

sm 10

m 3732

a

d2 t

2

Example of free-fall:

initial

final

v= vo + at = 0 + (10m/s2)(8.64s) = 86.4m/s

= 86.4 m/s (1/1000 km/m)(1/1.61 mile/km)(3600 s/hr)

= 193 mph

• Motion with Uniform (Constant) Acceleration • Motion with Uniform (Constant) Acceleration

Main Points from Today’s Lecture

• Free fall

d = d0 + v0t + 1/2at2 d = d0 + v0t + 1/2at2

Initial distance at t = 0

accelerationInitial

velocity: velocity at t

= 0

v= vo + atv= vo + at

Initial velocity:

velocity at t = 0

accelerationFinal

velocity

How long does it take to drop things How fast are they going at any given time?

How long does it take to drop things How fast are they going at any given time?

HW

Re-Read Ch 3

Make sure you understand all example problems done in class