1. LESSON 12 Acceleration Δt Δt
ACCELERATION (a) is defined as the rate in change of velocity, i.e. how fast does the speed of an object (Δv) change over time (Δt).
a = Δv a = v2 - v1
Δt Δt
If you look at the equation, the units look a little bit funny. If you were measuring speed in m/s and time in s, then the units for acceleration are m/s/s, or m/s2, read as "metres per second per second," "or metres per second squared.“
If you had an acceleration of 5 m/s2, then your speed would increase by 5 m/s every single second. If you started from rest, after 1 second, your speed would be 5 m/s. After 2 seconds, your speed would be 10 m/s. After 3 seconds, your speed would be 15 m/s, and so on.

2. PROBLEM: A motorcycle accelerates to 25
PROBLEM: A motorcycle accelerates to 25.6 m/s [W] from rest in a time of 3.4 s. What is the motorcycle's acceleration.

3. DECELERATION occurs when an object slows down, i. e
DECELERATION occurs when an object slows down, i.e. decreases its speed. This is also called NEGATIVE ACCELERATION. Whenever acceleration has a negative sign, it means the object is slowing down. With vectors, this means the acceleration is in the opposite direction.
PROBLEM: A boat moving at 19.3 m/s [N] decelerates to 10.2 m/s [N] in 4.5 seconds. Determine the boat's acceleration.

4. PRACTICE: Supercars are known for their powerful acceleration, but also powerful braking. The McLaren F1 can go from a velocity of 27.8 m/s [S] to a stop in a mere 5.2 seconds. What is its average acceleration?

5. CONSTANT ACCELERATION occurs when the same change in velocity (Δv) occurs in each equal interval of time (Δt), i.e. if the acceleration is 6.8 m/s2, then it remains 6.8 m/s2, it never changes.
AVERAGE ACCELERATION (aav) occurs when acceleration varies over a period of time, i.e. it looks at your initial and final velocity, without considering the speeding up and slowing down in between.
Suppose you are in a car at rest. As it speeds up, you can feel the acceleration as you get sucked into your seat (this sensation is known as a g-force). If this force remains constant and doesn't change, you have experienced constant acceleration for a period of time. You may study this more later on in the physics unit.
Constant acceleration usually does not last very long since most objects have an upper speed limit, and must top out their speed instead of continuing to accelerate.
If you are in a car that is constantly going faster and slower, you are experiencing average acceleration. When a car jerks around, this is occurring (very rapidly).

7. Recall the equation for calculating acceleration:
a = v2 - v1 Δt
How can we use this equation to solve for the initial speed, final speed, or time? We can rearrange this equation using algebra.
a = v2 - v1 - Multiply both sides by Δt.
- Divide both sides by a.

8. a = v2 - v1 - Multiply both sides by Δt.
- Add v1 to both sides.
- Subtract aΔt from both sides.

9. PRACTICE: A car is attempting to merge onto a highway
PRACTICE: A car is attempting to merge onto a highway. It is travelling 12.7 m/s [N] on the on-ramp, and accelerates to 27.4 m/s [N] in order to merge. If the car has an average acceleration of 4.3 m/s2 [N], how long does this take?

10. PRACTICE: A truck slows down at a rate of 5. 48 m/s2 [W] for 2. 40 s
PRACTICE: A truck slows down at a rate of 5.48 m/s2 [W] for 2.40 s. If the truck's initial velocity was 24.3 m/s [E], what was its final velocity?

11. PRACTICE: A car attempting to avoid a crash slams on its brakes to a stop. It takes the car 3.4 s to complete the stop with an average acceleration of 11.2 m/s2 [N]. What was the car’s initial velocity?
H.W. Worksheet 12