Kinematics Study Guide
Mastering 1D Motion at Panda Academy
Welcome to your Kinematics guide.
What is Kinematics?
Everything around us in motion .Kinematics is the branch of physics that describes the motion of points, bodies, and systems without considering the forces that cause them to move.In this chapter we focus on 1 DIMENSIONAL MOTION (1D)
Scalars and Vector
All physical quantities ( anything that can be measured i.e length,mass, temperature ) is of two types scalar & vectors.
- Scalars: Quantities that only have magnitude (size), such as distance, speed, and time,temperature,density.
- Vectors: Quantities that have both magnitude and direction, such as displacement, velocity, and acceleration.
Distance vs. Displacement
- Distance: The total path length traveled by an object. It is a scalar meaning we don’t care about the direction.It s always a positive a number.In SI system units : m,cm
- Displacement: The straight-line change in position from start to finish. It is a vector meaning we consider both magnitude along with the direction. It can be +ve,-ve or Zero.In SI system unit : m,cm
Example 1: Joshua biking to school
Imagine Joshua biking to reach to school.
1. Calculating Total Distance:
Distance is the total path covered.
Distance = 400m + 300m = 700 meters.
2. Calculating Displacement:
Displacement is the straight-line distance from the start to the end point.
Displacement = √(400² + 300²) ≈ 500 meters towards north west
Example 2: A Swimmer in a Pool
Imagine a swimmer in a 50-meter long pool.
1. One-Way Trip (Single Lap):
The swimmer swims from one end to the other.
Distance = 50 meters.
Displacement = 50 meters (forward).
2. Round Trip (Back to Start):
The swimmer swims to the end and returns to the initial starting position.
Total Distance = 50m + 50m = 100 meters.
Displacement = 0 meters.
Speed vs. Velocity
- Speed: The rate at which an object covers distance. It is a scalar quantity.
Average Speed = Total Distance / Total Time
- Velocity: The rate at which an object changes its position. It is a vector quantity (includes direction).
Average Velocity = Displacement / Time
Example 3: Speed and Velocity of the Swimmer
Let’s use the Round Trip example from above. Suppose the swimmer takes 100 seconds to swim the full 100 meters (back to the start).
1. Calculating Average Speed:
Total Distance = 100m, Total Time = 100s.
Average Speed = 100 m / 100 s = 1 m/s
2. Calculating Average Velocity:
Total Displacement = 0m (since they are back at the start), Total Time = 100s.
Average Velocity = 0 m / 100 s = 0 m/s
Conclusion: Even though the swimmer was moving fast, their average velocity is zero because they ended up exactly where they started!
Acceleration
- Definition: Acceleration is the rate at which an object changes its velocity. Since it depends on velocity, it is a vector quantity.
- Formula:
Acceleration = Change in Velocity / Time = (v_final – v_initial) / t
- Units: The SI unit for acceleration is meters per second squared (m/s²).
Example 4: A Car Speeding Up
Imagine a car starting from rest (0 m/s) and reaching a velocity of 20 m/s in 5 seconds.
Calculating Acceleration:
Initial Velocity (v_i) = 0 m/s, Final Velocity (v_f) = 20 m/s, Time (t) = 5s.
a = (20 m/s – 0 m/s) / 5 s = 4 m/s²
Conclusion: The car increases its velocity by 4 meters per second every second.