Speed, velocity and acceleration

Physics 100 Chapter 2

speed

speed = v =distance traveled

elapsed time

50km

v = 50km1 hr = 50km/hr

Hawaii Kai HaleiwaIn one hour

This is the averagespeed over 1 hour.For shorter time intervals it can be higher or lower.

Earth’s motion around the Sun

r=1.5x1011m

V = distance

elapsed time = 2 r 2 x 3.14 x 1.5 x 1011m

365 days x 24 hrs/day =

1year

= 9.4 x 1011 m8760 hrs

=9.4 x 1011 m

8.76 x103 hrs= 1.1x108 m/hr

= 1.1x105 km/hr 70,000 mi/hr

Velocity = speed + direction

r=1.5x1011m

6 months laterspeed = same

different directionv

velocity is a “vector”: a quantity that has both magnitude and direction

Length of the arrow = speedDirection of arrow same asdirection of the motion

Scalars and Vectors

Simple numbers:

Speed vTemperature T

Number + direction

Velocity vrelative positions rForce FAcceleration a

PSB

r CampusCenter

Acceleration ( changes in v)

acceleration =change in velocity

elapsed time

a =change in velapsed time

Change in V = 100km/hr

Elapsed time = 3 sec

“This baby goes from 0 to100km/hr in only 3 seconds”

a =change in velapsed time

=100km/hr

3 s = 33 km/hr s

103 m

3600 s=3.6x103s

=33x103m

3.6x103 sxs = 9.1 m/s2

Different ways to change V

v v

Car speeds up

v

Car slows up

vscreech!

a

a

Accelerations (continued)

v

Car turnsv

In all three cases, v changes. Therefore these are all examples of accelerations

a

Free Fall

5m

t=0 v0=0

t=1s v1=?

vavg = disttime

5m1 s

= = 5m/s

vavg = v0 + v1

2

0 + v1

2=

v1

2=

v1 = 2vavg = 10 m/s

V1 = 10 m/s

Free-fall acceleration

acceleration =change in velocity

elapsed time

a = 10m/s1s = 10 m/s2

10m/s

1s

This is called the “acceleration due to gravity” and given the special symbol:

g=10m/s2

Actually g=9.8m/s2. But 10 m/s2 is close enough for us.

g

Free fall from greater heights

V0 = 0

t = 0s

V1 = 10m/s

t = 1s

5m

V2 = 20m/s

t = 2s

V3 = 30m/s

t = 3s

V4 = 40m/s

t = 4s

15m

25m

35m

5m

20m

45m

80m

Total distance

12

gt2

Upward tossV4 = 0t = 4s

V3 = 10m/st = 3s5m

V2 = 20m/st = 2s

V1 = 30m/st = 1s

V0 = 40m/st = 0

15m

25m

35m

75m

60m

35m

0m

Total height

80m

gt212

v0t-

Simple rule for free fallaka: projectile motion

When Earth’s gravity is the only force involved:

actual height = height for no gravity – ½gt2

Horizontal tosst = 0s

t = 1s

5m

t = 2s t = 3s t = 4s

20m

45m

80m

upward toss

t = 0s

t = 1s

5m

t = 2s

t = 3st = 4s

20m

45m80m

Shoot the monkeycommunistdead whiteEuropean male

Shoot the DWEM: Slower bullet

Very fast horizontal toss

t = 0s

t = 1sx= 8km

5m

t = 2sx=16km

t = 3sx=24km

20m 45m

V=8km/s

Orbital motion is free fall

Artificial satellite

Turning car

An object free to slide on the dashboard,tries to follow a straight line path