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Equations of Motion

Part of the Mechanics section of Coddy's Physics journey. Lesson 30 of 97.

For a constant acceleration:

$\relax v = v_0 + a t$

$\Delta x = v_0 t + \tfrac12 a t^2$

$v^2 = v_0^2 + 2 a \Delta x$

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

$\Delta x$ = rectangle + triangle = v0 t + ½ a t².

Challenge

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

Try it yourself

Physics diagram: cart; arrows v 0 = 6 m/s, a = ?

Solve for $a$

Test yourself

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

All lessons in Mechanics

1Introduction

What is Physics?Your First Equation Turning a Rule Around

4Inclined Planes

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

7Projectile Motion

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

10Work and Energy

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

13Impulse and Momentum

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

16Simple Harmonic Motion

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

2Vectors 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

5Kinematics in 1D

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

8Kinematics and Newton

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

11Springs

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

14Momentum in 2D

Momentum as a Vector 2D Collisions Explosions Recap - Billiards

17Gravitation

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

3Friction

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

6Vertical Motion

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

9Project: Delivery Drone

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

12Elastic Energy

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

15Circular Motion

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

18Final Challenges

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