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Average velocity, Derive equations of motion from the graph, Equations of motion for uniformly accelerated motion, Solving kinematics problems

1.
Equations of Uniform

Accelerated Motion

Mr. Berman

Accelerated Motion

Mr. Berman

2.
Average Velocity

v = ½ (vf +vi)

v = ½ (vf +vi)

3.
•Displacement in terms of Average

Velocity and Time

d= v t

d= ½ (vf + vi) t

Velocity and Time

d= v t

d= ½ (vf + vi) t

4.
How do we derive d= ½ (vf + vi)t from the

vf

vi

o

t Time (s)

•Hint: Area Under the Line=Displacement Δd or simply d

vf

vi

o

t Time (s)

•Hint: Area Under the Line=Displacement Δd or simply d

5.
Displacement (d) in terms of vi , a, t

d= vit + ½ at2

d= vit + ½ at2

6.
How do we derive d= vit + ½ at2 ?

Hint: Start with d= ½ (vf + vi)t and then

substitute for vf that vf = vi+at.

Hint: Start with d= ½ (vf + vi)t and then

substitute for vf that vf = vi+at.

7.
•Final Velocity in terms of vi, a, d

vf2 = vi2 + 2ad

vf2 = vi2 + 2ad

8.
How do we derive vf2 = vi2 + 2ad ?

Hint: Start with d= ½ (vf + vi)t and then

substitute for t = (vf – vi) /a .

Hint: Start with d= ½ (vf + vi)t and then

substitute for t = (vf – vi) /a .

9.
vf= vi+ at

vavg = ½ (vf +vi)

of Motion d= ½ (vf + vi)t

for Uniform d= vit + ½ at2

Motion vf2 = vi2 + 2ad

d is the displacement (or

Δd)

Assume that ti=0

vavg = ½ (vf +vi)

of Motion d= ½ (vf + vi)t

for Uniform d= vit + ½ at2

Motion vf2 = vi2 + 2ad

d is the displacement (or

Δd)

Assume that ti=0

10.
Solving Kinematics Problems

Draw a labeled vector diagram showing the

positive and negative direction.

Make a list of the givens (include signs as

needed) and unknown.

Decide what equation(s) you should use.

Write the equation(s) and solve for the

unknown. Always include units in your first

substitution and in your final answer.

Draw a labeled vector diagram showing the

positive and negative direction.

Make a list of the givens (include signs as

needed) and unknown.

Decide what equation(s) you should use.

Write the equation(s) and solve for the

unknown. Always include units in your first

substitution and in your final answer.

11.
Problem 1

A rocket travelling at +95m/s is

accelerated uniformly to +150m/s in 10s.

What is the displacement?

A rocket travelling at +95m/s is

accelerated uniformly to +150m/s in 10s.

What is the displacement?

12.
Problem 2

An airplane has a minimum take off

velocity of 80m/s. How long should the

runway be, if the airplane can accelerate

on the ground at 3m/s2 ?

Answer: 1,067m

An airplane has a minimum take off

velocity of 80m/s. How long should the

runway be, if the airplane can accelerate

on the ground at 3m/s2 ?

Answer: 1,067m

13.
Problem 3

An airplane landing at +100m/s, comes to

a stop in 30s.

1. What is the acceleration?

2. How far did it travel on the runway before it

stopped?

Answer: -3.3m/s2, 1,515m

An airplane landing at +100m/s, comes to

a stop in 30s.

1. What is the acceleration?

2. How far did it travel on the runway before it

stopped?

Answer: -3.3m/s2, 1,515m