Equations of Uniform Accelerated Motion

1
Equations of Uniform Accelerated Motion

• Physics
• Mrs. Coyle

2
Average Velocity
?

• v ½ (vf vi)

3
Displacement in terms of Average Velocity and
Time
?

• d v t
• d ½ (vf vi) t

4
How do we derive d ½ (vf vi)t from the graph?
vf
Velocity (m/s)
vi
o
Time (s)
t

• Hint Area Under the LineDisplacement ?d or
  simply d

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

• 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 viat.

7
Final Velocity in terms of vi, a, d

• 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 .

9
Equations of Motion for Uniform Accelerated Motion

• vf vi at
• vavg ½ (vf vi)
• d ½ (vf vi)t
• d vit ½ at2
• vf2 vi2 2ad
• d is the displacement (or ?d)
• Assume that ti0

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 unkown.
• 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?
• Answer1,225.m

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

13
Problem 3

• An airplane landing at 100m/s, comes to a stop
  in 30s.
• What is the acceleration?
• How far did it travel on the runway before it
  stopped?
• Answer -3.3m/s2, 1,515m