Key Concepts

• Velocity: The rate of change of an object's position with respect to time. It is a vector quantity and includes both the speed and direction of the object's motion.
• Speed: The distance traveled per unit of time. It is a scalar quantity and only includes the magnitude of the object's motion, not the direction.
• Acceleration: The rate of change of an object's velocity with respect to time. It can be positive (speeding up), negative (slowing down), or zero (constant velocity).
• Distance: The total length of the path traveled by an object, regardless of direction.
• Displacement: The change in position of an object from its initial point to its final point. It is a vector quantity that includes both the magnitude and direction of the change in position.

Equations

1. Velocity: \( v = \frac{\Delta x}{\Delta t} \)
2. Acceleration: \( a = \frac{\Delta v}{\Delta t} \)
3. Distance: \( d = v \times t \)
4. Displacement: \( \Delta x = v \times t \)

Example Problems

1. A car travels at a constant speed of 60 km/h for 2 hours. What is the total distance traveled by the car?

2. A train accelerates from rest at a rate of 2 m/s². How long will it take for the train to reach a velocity of 20 m/s?

3. A runner sprints in a straight line for 100 meters, then turns around and runs back to the starting point. What is the runner's total displacement?