Kinematics

Introduction

• Kinematics refer to the mathematical description of motion.

  Position (x)

  Time interval (Δt)

  Displacement (change in position)

  Velocity (Δd/Δt)

  Acceleration (Δv/Δt)

• Described using one of two types of quantities:

  • Scalars: described only by numerical value (e.g. time is 4 seconds)
  • Vectors: described by both numerical and directional value (e.g. velocity is 4 m/s due west)

The Big 4 Equations

These 4 equations will allow you to solve all of the kinematic problems you could encounter.

1. $v=v_0 + at$
2. $\Delta x = (\frac{v+v_0}{2})t$
3. $\Delta x = v_0t + \frac{1}{2}at^2$
4. $v^2 = v_0^2 + 2a\Delta x$

Projectile Motion

Projectile motion describes the motion of a object (projectile) along a path in the air (trajectory), subject only to acceleration of gravity.

<aside> 💡 In these problems remember that horizontal motion doesn’t affect vertical motion and that the only acceleration is gravity. Acceleration due to gravity is 9.8 $m/s^2$

</aside>

Motion in each direction can be calculated separately which makes the math much simpler. Split it up using the follow two equations:

1. $V_x = v cos(\theta)$
2. $V_y = v sin(\theta)$

Example Problem:

A power cell is launched at 30 m/s at an angle of 60°. What’s the maximum height the power cell will reach?

• Solution

Force