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