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Unit 2: Motion in One Dimension

Position, velocity, and acceleration, and the graphs that draw the whole story of a moving object without a single equation.

7 topics · 29 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Distance and Displacement

  1. How it worksHow does displacement only care about start and end points while distance tracks the whole path?
  2. Worked exampleFind the displacement of a hiker who walks 6 km east and then 2 km west.
  3. Common mistakeWhy isn't total distance traveled the same number you'd use to find average velocity?
Your turn1 of 2
Find the displacement of a hiker who walks 21 km east and then 10 km west.

Speed and Velocity

  1. How it worksHow does average velocity divide total displacement by total time instead of distance by time?
  2. Worked exampleFind the average velocity of a car that drives 150 km east in 2 hours.
  3. Common mistakeWhy isn't instantaneous speed the same as average speed over a whole trip?
  4. Going furtherWhat happens to average velocity when a trip ends at the same place it started?
Your turn1 of 2
A car's speedometer needle climbs to 60 miles per hour whether the car is heading north on a highway or looping around a curve back toward the south, showing the exact same number either way. Why does a speedometer never tell you which way the car is going?

Reading Position-Time Graphs

  1. How it worksHow does the slope of a position-time graph at any instant give you the velocity right there?
  2. Worked exampleFind the velocity of an object whose position-time graph rises from 0 to 20 meters in 4 seconds.
  3. Worked exampleFind the average velocity between t=2s and t=6s on a position-time graph that goes from 10 m to 30 m.
  4. Common mistakeWhy doesn't a position-time graph that curves downward mean the object is slowing down?
Your turn1 of 2
Find the velocity of an object whose position-time graph rises from 0 to 141 meters in 13.16 seconds along a straight line.

Reading Velocity-Time Graphs

  1. How it worksHow does the slope of a velocity-time graph tell you the acceleration at every instant?
  2. Worked exampleFind the distance traveled by an object whose velocity-time graph is a flat line at 10 m/s for 5 seconds.
  3. Worked exampleFind the distance traveled by an object whose velocity-time graph climbs in a straight line from 0 to 20 m/s over 8 seconds.
  4. Common mistakeWhy doesn't a velocity-time graph crossing zero mean the object has stopped moving forever?
Your turn1 of 2
Find the distance traveled by an object whose velocity-time graph is a flat line at 42 m/s for 26 seconds.

Acceleration

  1. How it worksHow does acceleration measure the rate at which velocity itself is changing?
  2. Worked exampleFind the acceleration of a car that speeds up from 10 m/s to 30 m/s in 4 seconds.
  3. Common mistakeWhy isn't an object with zero velocity necessarily an object with zero acceleration?
  4. Going furtherWhat happens to the sign of acceleration when a car slows down while moving in the negative direction?
Your turn1 of 2
Find the acceleration of a car that speeds up from 14 m/s to 46 m/s in 14.02 seconds.

The Kinematics Equations

  1. How it worksHow do the kinematics equations connect position, velocity, acceleration, and time without calculus?
  2. Worked exampleFind how far a car travels while accelerating from 5 m/s to 25 m/s at 4 m/s2.
  3. Worked exampleFind the time it takes a ball thrown upward at 15 m/s to return to the same height it started from.
  4. Common mistakeWhy can't you use the constant-acceleration equations on a trip where the acceleration keeps changing?
  5. Going furtherWhat happens to the kinematics equations when the acceleration is exactly zero?
Your turn1 of 2
Find how far a car travels while accelerating from 10 m/s to 38 m/s at 9 m/s2.

Free Fall

  1. How it worksHow does gravity give every falling object the same acceleration no matter its mass?
  2. Worked exampleFind how long it takes an object dropped from rest to fall 45 meters.
  3. Common mistakeWhy doesn't a bowling ball fall faster than a tennis ball dropped from the same height?
  4. Common mistakeWhy doesn't crumpling a sheet of paper before dropping it prove that mass changes free-fall speed?
  5. Ties togetherHow does free fall turn into just the vertical half of projectile motion once an object is launched sideways?
Your turn1 of 2
Find how long it takes an object dropped from rest to fall 140 meters, using g = 9.8 m/s2.