Instantaneous velocity

Graphically

Calculus

Position from Velocity

Graphically

Calculus

Motion with Constant Acceleration

Find the average velocity for this motion from:

a) t=1-3

b) t=0-3

c) t=3-6

d) t=0-6

Find the instantaneous velocities at times

a) t=2

b) t=4.9

c) t=4.3

20 m/s

-26.7 m/s

0 m/s

20 m/s

13.3 m/s

-13.3 m/s

0 m/s

**Find the:**

**a) position at t = 3 s**

b) velocity at t = 3 s

c) acceleration at t = 3 s

b) velocity at t = 3 s

c) acceleration at t = 3 s

**Harder:**

a) time when velocity is zero

b) location when velocity is zero

c) acceleration at those locations

a) time when velocity is zero

b) location when velocity is zero

c) acceleration at those locations

**76 m**

78 m/s

54 m/s^2

78 m/s

54 m/s^2

**+/- .577 s**

2.85 m 5.15 m

+/- 10.4 m/s^2

2.85 m 5.15 m

+/- 10.4 m/s^2

If the initial position is x = 0 m

at what time(s) is the particles location at

x = 20 m

x = 35 m

x = 17.5 m

if the initial position is x = 0 m

where is the particle at

t = 2 s

t = 4 s

3.74 s

6 s and 10 s

4 s and 12 s

5 m

20 m

a particle's velocity is described by the function

what is the equation for its position if it starts at a location of 12 m

What is the equation for its acceleration?

At what time does the particle reach its turning points?

What is the location and acceleration at those points?

t = 2, 5 s

x=20.7 ,16.2 m

a=-3 , 3 m/s^2

what is her acceleration in the ice?

3.5 m/s^2

What is the speed at take off?

How far does it travel in the first second?

How far does it travel in the last second?

What percent of the final speed is its speed in the middle?

26.8 s

134 m/s

2.5 m

132 m

71 %

"I still don't understand what how to get the area under the line on a graph, or why its needed or important."

Position

x

velocity

v

acceleration

a

graphically: slope

math: derivative

graphically: slope

math: derivative

graphically: area

math: integral

graphically: area

math: integral

"The examples of motion with constant acceleration don't seem to hard, will we do any with a varying acceleration and if so how would we approach that?"

"I don't understand how by looking at a word problem you can decide on what equation to use. "

120 m

what is the minimum stopping distance if the initial speed is 40 m/s