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?

Time (s)o

Velocity (m/s)

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

vf

vi

t

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 = vi

2 + 2ad

How do we derive vf2 = vi

2 + 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 = vi

2 + 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

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