Transcript Document

Equations of Uniform
Accelerated Motion
Physics
Mrs. Coyle
Average Velocity
v = ½ (vf +vi)
•Displacement in terms of Average
Velocity and Time
d= v t
d= ½ (vf + vi) t
How do we derive d= ½ (vf + vi)t from
the graph?
Velocity
(m/s)
vf
vi
o
t
Time (s)
•Hint: Area Under the Line=Displacement Δd or simply d
Displacement (d) in terms of vi , a, t
d= vit + ½ at2
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.
•Final Velocity in terms of vi, a, d
vf2 = vi2 + 2ad
How do we derive vf2 = vi2 + 2ad ?

Hint: Start with d= ½ (vf + vi)t and then
substitute for t = (vf – vi) /a .
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
Δd)
 Assume that ti=0

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.

Problem 1
A rocket travelling at +95m/s is
accelerated uniformly to +150m/s in 10s.
What is the displacement?
Answer:1,225.m
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
Problem 3
1.
2.
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