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### 302-B: The Acceleration Formula

• Topic Cluster: Kinematics
• Topic: Forward Kinematics Quantitative
• Objective: Solve for acceleration using its definition.
• Content: Acceleration is equal to change in velocity divided by change in time.
• Level: 1

#### BACK to Ladder Forward Kinematics Quantitative

The previous formula, distance = speed * time, is useful if an object is moving at a constant velocity. However, most interesting physics involves objects that are either speeding up or slowing down. To analyze these objects, we need a new quantity, the acceleration. In this pod, we will learn the formula that defines acceleration.

$$a = \frac{v_f - v_i}{\Delta t}$$

The unit of acceleration can be written as meters per second per second (m/s/s), or as meters per second-squared (m/s2). Even though there is a square in the unit, it does not mean you need to square the value. Treat it like any other unit.

1. I have an initial velocity of 10 m/s. I have a final velocity of 40 m/s. A time of 5 seconds passes. What is my acceleration?
2. I have an initial velocity of 2 m/s. I have a final velocity of 26 m/s. A time of 6 seconds passes. What is my acceleration?
3. I have an initial velocity of 7 m/s. I have a final velocity of 57 m/s. A time of 10 s passes. What is my acceleration?
##### "At Rest"

When a problem says something is at rest, it means that velocity is equal to zero. If it begins at rest, initial velocity is zero. If the ends at rest, final velocity is zero.

1. I begin at rest. I have a final velocity of 40 m/s. A time of 5 s passes. What is my acceleration?
##### Negative Acceleration

Acceleration can be either positive or negative. When it is positive, it means something is speeding up. When it is negative, it means something is slowing down. Sometimes, negative acceleration is called deceleration, but most physicists prefer the term negative acceleration.

1. A car has an initial velocity of 24 m/s. It has a final velocity of 10 m/s. A time of 7 s passes. What is its acceleration?
2. I have an initial velocity of 50 m/s. I slow down until I am at rest. A time of 10 s passes. What is my acceleration?
3. Acceleration is positive. Which is greater, initial velocity or final velocity?
4. Acceleration is negative. Which is greater, initial velocity or final velocity?

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