In physics, speed, velocity, and acceleration are three fundamental concepts that describe the motion of objects. This worksheet will help you understand these concepts in more detail and solve problems involving them.
Speed
Speed is a scalar quantity that measures the rate at which an object is moving. It is the distance traveled per unit time. The SI unit of speed is meters per second (m/s).
Formula for Speed
Speed = Distance / Time
Example: A car travels 100 kilometers in 2 hours. The speed of the car is:
Speed = 100 km / 2 h = 50 km/h
Velocity
Velocity is a vector quantity that measures the rate at which an object is moving in a specific direction. It is the displacement per unit time. The SI unit of velocity is meters per second (m/s).
Formula for Velocity
Velocity = Displacement / Time
Example: A ball is thrown vertically upward with an initial velocity of 10 m/s. The displacement of the ball after 2 seconds is:
Displacement = 10 m/s * 2 s = 20 m
The velocity of the ball after 2 seconds is:
Velocity = 20 m / 2 s = 10 m/s
Acceleration
Acceleration is a vector quantity that measures the rate at which an object’s velocity is changing. It is the change in velocity per unit time. The SI unit of acceleration is meters per second squared (m/s^2).
Formula for Acceleration
Acceleration = (Final Velocity - Initial Velocity) / Time
Example: A car accelerates from rest to a speed of 60 km/h in 10 seconds. The acceleration of the car is:
Acceleration = (60 km/h - 0 km/h) / 10 s = 6 km/h/s
Relationships Between Speed, Velocity, and Acceleration
Speed, velocity, and acceleration are related to each other by the following equations:
Velocity = Speed * Direction
Acceleration = (Final Velocity - Initial Velocity) / Time
Common Mistakes to Avoid
When working with speed, velocity, and acceleration, it is important to avoid the following common mistakes:
- Confusing speed with velocity: Speed is a scalar quantity that measures the rate at which an object is moving, while velocity is a vector quantity that measures the rate at which an object is moving in a specific direction.
- Confusing acceleration with speed: Acceleration is a vector quantity that measures the rate at which an object’s velocity is changing, while speed is a scalar quantity that measures the rate at which an object is moving.
- Using the wrong units: The SI units for speed, velocity, and acceleration are meters per second (m/s), meters per second (m/s), and meters per second squared (m/s^2), respectively.
Practice Problems
- A car travels 200 kilometers in 4 hours. What is the speed of the car?
- A ball is thrown vertically upward with an initial velocity of 15 m/s. The displacement of the ball after 3 seconds is:
- A car accelerates from rest to a speed of 70 km/h in 12 seconds. The acceleration of the car is:
- A car is traveling at a speed of 60 km/h when it applies the brakes and comes to a stop in 5 seconds. The acceleration of the car is:
Answers to Practice Problems
- 50 km/h
- 45 m
- 5.83 km/h/s
- -12 km/h/s