Section 3
Acceleration
Acceleration
We can change the state of motion of an object by
changing its speed, direction, or both.
Acceleration is the rate at which the velocity is changing.
Acceleration
In physics, the term acceleration applies to decreases as
well as increases in speed.
When a car speeds up, that is
positive acceleration!
When a car slows down, that is
negative acceleration or
deceleration!
Acceleration
A car is accelerating whenever there is a change in its state
of motion.
Acceleration
Change in Direction
Acceleration also applies to changes in direction.
§  It is important to distinguish between speed and velocity.
§  Acceleration is defined as the rate of change in velocity, rather
than speed.
§  Acceleration, like velocity, is a vector quantity because it is
directional.
Acceleration
A softball accelerates when it is thrown, hit, or caught. What
change in motion occurs in each example?
§  Thrown-ball: Speeds Up
§  Hit-ball: Changes direction
§  Caught-ball: Slows Down - Decelerates
Acceleration
Change in Speed
When straight-line motion is considered, it is common to use
speed and velocity interchangeably.
When the direction is not changing, acceleration may be
expressed as the rate at which speed changes.
Acceleration Formula
Acceleration = ∆ velocity
Time
a = (vF – vI)
t
VF = final velocity
VI = initial velocity
t = time
Units: m/s2, km/hr2, ft/s2
Example #1
A motorcycle starts at rest and accelerates to 80 m/s in 20
seconds. What is the acceleration of the motorcycle?
a = ( Vf – Vi ) / t = (80 m/s – 0 m/s) / 20s
a= 4 m/s2
Example #2
A skateboarder moves in a straight line at 3 m/s and comes to
a stop in 2 s. What is their acceleration?
a = ( Vf – Vi ) / t
a = (0 m/s – 3 m/s) / 2s
a = -1.5 m/s2 (deceleration)
Kinematic Equations
The Big “5”
Kinematic Equations
Kinematics is a branch of physics that studies motion. With these equations and what we now
know about displacement, time, velocity and acceleration we can calculate any of these if
unknown. Notice on the right side the variable that is not in the equation to the left. This helps
in determining the right equation.
WhoCares
V f = Vi + a ⋅ t
Δd
d = Vi ⋅ t + 1 2 a ⋅ t 2
Vf
1
d = (Vi + Vf ) ⋅ t
2
a
2
2
= Vi + 2a ⋅ d
Δt
d = V f ⋅ t − 12 a ⋅ t 2
Vi
Vf
Example #3
A box slides down an incline with uniform acceleration. It starts
from rest and attains a speed of 2.7 m/s in 3 seconds.
Find:
a.  The acceleration
b.  The distance moved in the first 6 seconds
Example #4
A truck moves from rest and moves with a constant
acceleration of 5 m/s2. Find the speed and the distance
traveled after 4 seconds.
Example #5
A car starts from rest and coasts down a hill with a
constant acceleration. If it goes 90 meters in 8 seconds,
find the acceleration of the car.
Example #6
A plane starts from rest and accelerates along the ground
before takeoff. It moves 600 m in 12 s.
Find:
a.  The acceleration
b.  Speed at the end of 12 seconds
c.  Distance moved during the 11th and 12th second