Mechanics · Quick Reference

Motion in One Dimension Cheat Sheet

Mechanics · Lesson 4/19

In one line: the simplest kind of motion happens along a single straight line — mastering it lays the groundwork for understanding motion in two and three dimensions.

Key Ideas

1Position, Displacement, and Distance. Position is where an object is; displacement is the change in position (a vector); distance is the total path length traveled (a scalar, always >= displacement's magnitude).

2Speed vs. Velocity. Speed = distance/time (scalar); velocity = displacement/time (vector, includes direction).

3Acceleration. The rate of change of velocity over time: a = (change in velocity)/(change in time), measured in m/s^2.

4The Equations of Motion (Constant Acceleration). v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as, where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement.

5Reading Motion Graphs. On a position-time graph, slope = velocity. On a velocity-time graph, slope = acceleration, and the area under the curve = displacement.

Worked Examples

A car starts at rest and accelerates at 3 m/s^2 for 5 seconds. Find its final velocity.

v = 15 m/s

A car starts at 10 m/s and accelerates at 2 m/s^2 for 4 seconds. Find the distance traveled.

s = 56 m

A car accelerates from 5 m/s to 25 m/s over a distance of 100m. Find its acceleration.

a = 3 m/s^2

Formulas

v = u + at

s = ut + (1/2)*a*t^2

v^2 = u^2 + 2*a*s

Practice Yourself

A car accelerates from rest at 4 m/s^2 for 3s. Find final velocity.

12 m/s

A car at 8 m/s accelerates at 2 m/s^2 for 5s. Find distance traveled.

s=8*5+0.5*2*25=40+25=65m

What does the slope of a position-time graph represent?

Velocity