Final Exam Review
Mechanics
Constant Acceleration
Average Acceleration
• Formula: aavg = Δv / t
•
or
•
aavg = (vf-vi) / t
• Both equations are equivalent, and either
can be used when it’s convenient.
Example
• A shuttle bus slows down with an average
acceleration of -1.8 m/s2. How long does
it take the bus to slow from 9.0 m/s to a
complete stop?
Example
• A shuttle bus slows down with an average
acceleration of -1.8 m/s2. How long does
it take the bus to slow from 9.0 m/s to a
complete stop?
• Givens
a = -1.8 m/s2
•
vi = 9.0 m/s
•
vf = 0 m/s
Example
• A shuttle bus slows down with an average
acceleration of -1.8 m/s2. How long does
it take the bus to slow from 9.0 m/s to a
complete stop?
• Givens
a = -1.8 m/s2
•
vi = 9.0 m/s
•
vf = 0 m/s
• aavg=(vf-vi)/t → -1.8m/s2=(0 - 9.0m/s) / t
• t = -9.0 / -1.8 = 5s
Practice
• Page 49- Practice B
• Complete the FIRST TWO problems.
Displacement with Const Accel.
• Formula: Δx = ½ (vi+vf)t
Example
• A racing car reaches a speed of 42 m/s. It then begins
a uniform negative acceleration, using its parachute
and braking system, and comes to rest 5.5s later.
Find the distance that the car travels during braking.
Example
• A racing car reaches a speed of 42 m/s. It then begins
a uniform negative acceleration, using its parachute
and braking system, and comes to rest 5.5s later.
Find the distance that the car travels during braking.
• Givens
vi = 42 m/s
•
vf = 0 m/s
•
t = 5.5 s
Example
• A racing car reaches a speed of 42 m/s. It then begins
a uniform negative acceleration, using its parachute
and braking system, and comes to rest 5.5s later.
Find the distance that the car travels during braking.
• Givens
vi = 42 m/s
•
vf = 0 m/s
•
t = 5.5 s
• Δx = ½ (vi + vf) t → Δx = ½ (42m/s + 0m/s)(5.5s)
•
Δx = 120m
Practice
• Page 53- Practice C
• Complete the FIRST TWO problems.
Velocity AND Displacement with
Const Acc.
• Formula: Δx = vit + ½ at2
•
vf = vi + at
• Problems of this type are often two step
problems (though not always)
Example
• A plane starting at rest at one end of a runway undergoes a uniform
acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at
takeoff? How long must the runway be for the plane to be able to
take off?
Example
• A plane starting at rest at one end of a runway undergoes a uniform
acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at
takeoff? How long must the runway be for the plane to be able to
take off?
• Givens vi = 0 m/s
•
vf = ?
a = 4.8 m/s2
Δx = ?
t = 15 s
Example
• A plane starting at rest at one end of a runway undergoes a uniform
acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at
takeoff? How long must the runway be for the plane to be able to
take off?
• Givens vi = 0 m/s a = 4.8 m/s2 t = 15 s
•
vf = ?
Δx = ?
• Step 1 vf = vi + at → vf = 0m/s +(4.8m/s2)(15s) = 72 m/s
Example
• A plane starting at rest at one end of a runway undergoes a uniform
acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at
takeoff? How long must the runway be for the plane to be able to
take off?
• Givens vi = 0 m/s a = 4.8 m/s2 t = 15 s
•
vf = ?
Δx = ?
• Step 1 vf = vi + at → vf = 0m/s +(4.8m/s2)(15s) = 72 m/s
• Step 2 Δx = vit + ½ at2
•
Δx = (0m/s)(15s) + ½ (4.8m/s2)(15s)2
•
Δx = 540 m
Practice
• Page 55- Practice D
• Complete the FIRST TWO problems.