Acceleration formula and examples

📚 Quick Study Guide

• ⏱️ Acceleration is the rate at which velocity changes over time.
• 📐 It's a vector quantity, meaning it has both magnitude and direction.
• 🧮 The average acceleration formula is: $a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t_f - t_i}$, where $v_f$ is the final velocity, $v_i$ is the initial velocity, $t_f$ is the final time, and $t_i$ is the initial time.
• ➕ If acceleration and velocity have the same sign, the object speeds up.
• ➖ If acceleration and velocity have opposite signs, the object slows down.
• 📏 The standard unit of acceleration is meters per second squared ($m/s^2$).
• 💡 Constant acceleration means the velocity changes at a steady rate.

Practice Quiz

1. What does acceleration measure?
1. A) The total distance traveled.
2. B) The rate of change of velocity.
3. C) The force applied to an object.
4. D) The mass of an object.
2. What is the formula for average acceleration?
1. A) $a = \frac{d}{t}$
2. B) $a = \frac{v_f + v_i}{2}$
3. C) $a = \frac{\Delta v}{\Delta t}$
4. D) $a = v * t$
3. An object accelerates from 5 m/s to 15 m/s in 2 seconds. What is its average acceleration?
1. A) 2.5 $m/s^2$
2. B) 5 $m/s^2$
3. C) 7.5 $m/s^2$
4. D) 10 $m/s^2$
4. If an object has a negative acceleration, it is always...?
1. A) Speeding up
2. B) Slowing down
3. C) Moving at a constant velocity
4. D) Changing direction
5. What are the standard units of acceleration?
1. A) meters per second (m/s)
2. B) meters (m)
3. C) meters per second squared ($m/s^2$)
4. D) seconds (s)
6. A car slows down from 30 m/s to 10 m/s in 5 seconds. What is its acceleration?
1. A) 4 $m/s^2$
2. B) -4 $m/s^2$
3. C) 5 $m/s^2$
4. D) -5 $m/s^2$
7. What does constant acceleration imply?
1. A) The velocity is constant.
2. B) The velocity changes at a steady rate.
3. C) The object is at rest.
4. D) The object is moving in a circle.