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📘 Lesson 4 of 19 · Mechanics

🚗 Motion in One Dimension

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

Course progress: 21%

01 Key Concepts

Position, 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).

Speed vs. Velocity

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

Acceleration

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

The 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.

Reading Motion Graphs

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

02 Key Formulas

03 Solved Examples

Example 1 A car starts at rest and accelerates at 3 m/s^2 for 5 seconds. Find its final velocity.
  1. Apply v=u+at with u=0, a=3, t=5.
  2. v = 0 + 3*5.
Answer: v = 15 m/s
Example 2 A car starts at 10 m/s and accelerates at 2 m/s^2 for 4 seconds. Find the distance traveled.
  1. Apply s=ut+(1/2)at^2 with u=10, a=2, t=4.
  2. s = 10*4 + 0.5*2*4^2 = 40 + 0.5*2*16.
  3. = 40+16.
Answer: s = 56 m
Example 3 A car accelerates from 5 m/s to 25 m/s over a distance of 100m. Find its acceleration.
  1. Apply v^2=u^2+2as: 25^2 = 5^2 + 2*a*100.
  2. 625 = 25 + 200a.
  3. 600 = 200a, so a = 3.
Answer: a = 3 m/s^2

04 Practice Questions

1A car accelerates from rest at 4 m/s^2 for 3s. Find final velocity.
12 m/s
2A 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
3What does the slope of a position-time graph represent?
Velocity
4What does the area under a velocity-time graph represent?
Displacement
5What is the difference between speed and velocity?
Speed is a scalar; velocity is a vector (includes direction)

📄 Motion in One Dimension — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet