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gurbir-singh / Blank Project

May 21, 2025 11:34
kinematics
mechanics
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Blank Project

A quick reference guide covering essential kinematics concepts, formulas, and graphs.

Basic Definitions

Distance and Displacement

Distance

Total length of the path traveled by an object. It’s a scalar quantity (magnitude only).

Displacement

The change in position of an object. It’s a vector quantity (magnitude and direction).

\Delta x = x_{final} - x_{initial}

Symbol

Distance: d
Displacement: \Delta x

Units

Meters (m)

Key Difference

Distance always increases; Displacement can be positive, negative, or zero.

Speed and Velocity

Speed

The rate at which an object is moving. It’s a scalar quantity.

speed = \frac{distance}{time}

Velocity

The rate at which an object changes its position. It’s a vector quantity.

velocity = \frac{displacement}{time}

Symbol

Speed: v
Velocity: \vec{v}

Units

Meters per second (m/s)

Average Speed/Velocity

Average Speed = (Total Distance) / (Total Time)
Average Velocity = (Total Displacement) / (Total Time)

Acceleration

Acceleration

The rate at which an object’s velocity changes over time. It’s a vector quantity.

acceleration = \frac{\Delta velocity}{time}

Symbol

\vec{a}

Units

Meters per second squared (m/s²)

Constant Acceleration

Implies the velocity changes at a uniform rate.

Kinematic Equations

Constant Acceleration Equations

Variables Definition

v

Final velocity

v_0

Initial velocity

a

Acceleration

t

Time

\Delta x

Displacement

Motion Graphs

Position vs. Time (x-t) Graphs

Slope

Represents the velocity of the object.

Straight Line

Indicates constant velocity.

Curve

Indicates changing velocity (acceleration).

Horizontal Line

Indicates the object is at rest.

Velocity vs. Time (v-t) Graphs

Slope

Represents the acceleration of the object.

Area under the curve

Represents the displacement of the object.

Straight Line

Indicates constant acceleration.

Horizontal Line

Indicates constant velocity (zero acceleration).

Curve

Indicates changing acceleration.

Acceleration vs. Time (a-t) Graphs

Area under the curve

Represents the change in velocity.

Horizontal Line

Indicates constant acceleration.

Line at zero

Indicates zero acceleration (constant velocity).

Problem-Solving Tips

General Strategies

  1. Read the problem carefully: Identify what is given and what you need to find.
  1. Draw a diagram: Visualize the situation to help understand the problem.
  1. Identify knowns and unknowns: List all known variables with their values and identify the unknown variable(s).
  1. Choose the appropriate equation(s): Select the kinematic equation(s) that relate the knowns and unknowns.
  1. Solve the equation(s): Substitute the known values into the equation(s) and solve for the unknown(s).
  1. Check your answer: Ensure the units are consistent and the answer makes sense in the context of the problem.

Dealing with Vectors

  1. Break vectors into components: Resolve vectors into their x and y components.
  1. Apply kinematic equations separately: Use kinematic equations for each component.
  1. Recombine components: Combine the components to find the resultant vector.