1. Section 2–4 Acceleration Acceleration is the rate change of velocity.
Acceleration is a vector quantity.
Acceleration is a vector quantity.
Whenever velocity changes, there is an acceleration.
Whenever velocity changes, there is an acceleration.
Even if speed is constant, but direction changes, the changing velocity means there is accelerated motion.
Even if speed is constant, but direction changes, the changing velocity means there is accelerated motion.
Even if speed is constant, but direction changes, the changing velocity means there is accelerated motion.
Even if speed is constant, but direction changes, the changing velocity means there is accelerated motion.
Even if speed is constant, but direction changes, the changing velocity means there is accelerated motion.

2. Acceleration & deceleration1 2 3 4 1 2 3 4
Acceleration
Acceleration
Deceleration
Deceleration
object’s velocity
increases
object’s velocity
increases
object’s velocity
decreases
object’s velocity
decreases +a –a

3. Review of position-time graphs
We saw before that a constant velocity plots as a straight line on a position-time graph, and accelerated motion plots as a curve.
Velocity-time graphs will of course look different.

4. Velocity-time graphs
Velocity-time graphs give a horizontal line for constant velocity in one direction.
Velocity-time graphs give a horizontal line for constant velocity in one direction.
Velocity-time graphs give a horizontal line for constant velocity in one direction.
They give a constant, but non-zero sloping line for accelerated motion.
They give a constant, but non-zero sloping line for accelerated motion.
They give a constant, but non-zero sloping line for accelerated motion.

5. Interpreting velocity-time graphs
On a velocity-time graph, the independent variable (x-axis) is still time, and has regular time intervals.
On a velocity-time graph, the independent variable (x-axis) is still time, and has regular time intervals.
On a velocity-time graph, the independent variable (x-axis) is still time, and has regular time intervals.
The dependent variable (y-axis) is velocity.
The dependent variable (y-axis) is velocity.
The slope of a velocity-time graph represents the change in velocity over the change in time, which is the acceleration.
The slope of a velocity-time graph represents the change in velocity over the change in time, which is the acceleration.
The slope of a velocity-time graph represents the change in velocity over the change in time, which is the acceleration.
The slope of a velocity-time graph represents the change in velocity over the change in time, which is the acceleration.
The slope of a velocity-time graph represents the change in velocity over the change in time, which is the acceleration.

6. Interpreting Slope velocity (m/s) velocity (m/s) time (s) time (s)
increasing velocity
lower acceleration
velocity (m/s)
velocity (m/s)
increasing velocity
higher acceleration
time (s)
time (s)
slope = zero
velocity (m/s)
velocity (m/s)
decreasing velocity
constant velocity
deceleration
zero acceleration
time (s)
time (s)

7. initial velocity vector
Average Acceleration
initial velocity vector
final velocity vector – ∆v v v a B = = ∆t t – t
The average acceleration of an object is the change in velocity (during some measurable time interval) divided by that time interval.
The average acceleration of an object is the change in velocity (during some measurable time interval) divided by that time interval.
The average acceleration of an object is the change in velocity (during some measurable time interval) divided by that time interval.
The average acceleration of an object is the change in velocity (during some measurable time interval) divided by that time interval.
The average acceleration of an object is the change in velocity (during some measurable time interval) divided by that time interval.
Standard units for acceleration are derived from m/s/s. The units are m/s2.
Standard units for acceleration are derived from m/s/s. The units are m/s2.
Standard units for acceleration are derived from m/s/s. The units are m/s2.

8. Instantaneous Acceleration
Instantaneous acceleration is the change in velocity at one instant in time.
Instantaneous acceleration is the change in velocity at one instant in time.
v(t + ∆t) – v(t) dv
lim a = = ∆t dt
∆t→0
Instantaneous acceleration is the derivative of the velocity.
Instantaneous acceleration is the derivative of the velocity.
Instantaneous acceleration is the derivative of the velocity.
It can be determined by finding the slope of the tangent line to any point on a velocity-time graph.
It can be determined by finding the slope of the tangent line to any point on a velocity-time graph.
It can be determined by finding the slope of the tangent line to any point on a velocity-time graph.
It can be determined by finding the slope of the tangent line to any point on a velocity-time graph.

9. The craziness of positive and negative acceleration
The sign on acceleration can relate to:
Acceleration and deceleration, or
Acceleration and deceleration, or
Acceleration and deceleration, or
Forward and reverse motion.
Forward and reverse motion.
Forward and reverse motion.
Positive acceleration can mean either acceleration to the right, or deceleration in the negative direction, +(+a) or –(–a) = +a.
Positive acceleration can mean either acceleration to the right, or deceleration in the negative direction, +(+a) or –(–a) = +a.
Positive acceleration can mean either acceleration to the right, or deceleration in the negative direction, +(+a) or –(–a) = +a.
Negative acceleration can mean either deceleration to the right, or acceleration in the negative direction, –(+a) or +(–a) = –a.
Negative acceleration can mean either deceleration to the right, or acceleration in the negative direction, –(+a) or +(–a) = –a.
Negative acceleration can mean either deceleration to the right, or acceleration in the negative direction, –(+a) or +(–a) = –a.