Equations of Motion

Part of the Mechanics section of Coddy's Physics journey. Lesson 27 of 94.

For a constant acceleration:

v = v0 + a t

Δx = v0 t + ½ a t²

v² = v0² + 2 a Δx

The second is the area under the v-t line. The third has no t: use it when the time is not given.

A velocity-time graph: a straight line from v0 at time 0 to v at time t; the area under it is a rectangle v0 times t plus a triangle one half a t squared

Δx = rectangle + triangle = v0 t + ½ a t².

Challenge

A cart moving at 6 m/s speeds up with a constant acceleration and covers d = 40 m in 4 s. Find its acceleration a.

Try it yourself

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Mechanics

1Vectors and Newton's Laws

Right Triangles What is a Vector?Adding Vectors Axes and Directions Vector Components Forces Around Us Friction and Tension Newton's First Law Newton's Second Law Newton's Third Law Recap - Net Force

4Kinematics in 1D

Position and Displacement Velocity Acceleration Motion GraphsEquations of MotionRecap - Braking Car

7Kinematics and Newton

From Forces to Motion From Motion to Forces Two-Stage Motion Recap - Elevator

10Springs

Hooke's Law Springs in Series Springs in Parallel Recap - Spring Scale

13Momentum in 2D

Momentum as a Vector 2D Collisions Explosions Recap - Billiards

16Gravitation

Law of Gravitation Gravity and Altitude Satellites Kepler's Laws Gravitational Energy Escape Velocity Satellite Energy Recap - Mission to Orbit

2Friction

What is Friction?Static Friction Kinetic Friction Friction and Newton's Laws Recap - Sliding Crate

5Vertical Motion

Free Fall Throwing Upward Time in the Air Recap - Dropped Ball

8Project: Delivery Drone

Mission Briefing Takeoff Thrust Climb to Altitude Cruise and Brake Package Drop

11Elastic Energy

Elastic Potential Energy Spring Launchers Energy with Springs Recap - Spring Launcher

14Circular Motion

Uniform Circular Motion Centripetal Acceleration Horizontal Circles Vertical Circles Loop the Loop Recap - Car on a Curve

17Final Challenges

Recap - Stunt Ramp Recap - Crash Test Recap - Space Probe

3Inclined Planes

Forces on an Incline Gravity Components Frictionless Incline Incline with Friction Will It Slide?Recap - Ramp Challenge

6Projectile Motion

Independent Axes Horizontal Launch Launch at an Angle Range and Max Height Recap - Hit the Target

9Work and Energy

Work Kinetic Energy Work-Energy Theorem Gravitational PE Conservation of Energy Power Recap - Roller Coaster

12Impulse and Momentum

Momentum Impulse Conservation of Momentum Elastic Collisions Inelastic Collisions Recap - Air Track

15Simple Harmonic Motion

What is SHM?Mass on a Spring The Pendulum SHM Graphs Energy in SHM Recap - Oscillator