Unit 1 Review: Study Guide (Topics 1.1-1.3)
Name: _______________________ Date: _______________________
Use this to check your own understanding before Topics 1.4-1.5 build on all of it. Show your work — a correct final answer with no work shown only earns partial credit if this gets collected.
Quick Formula Reference
- Average velocity: $v_{avg} = \dfrac{\Delta x}{\Delta t}$
- Average speed: $\dfrac{\text{total distance}}{\text{total time}}$
- Acceleration: $a = \dfrac{\Delta v}{\Delta t}$
- Position-time graph: slope = velocity
- Velocity-time graph: slope = acceleration, area under curve = displacement
1. Distance vs. Displacement
A hiker walks 5 km east, then 2 km west. Find the total distance traveled and the displacement (with direction).
2. Vectors vs. Scalars
Label each quantity as a vector or a scalar: (a) "12 m/s" (b) "12 m/s north" (c) "30 minutes" (d) "3 km southeast"
3. Average Velocity and Average Speed
A cyclist rides 20 km north in 1 hour, then rides 20 km south back to the start in 1 hour. Find the average speed and average velocity for the entire trip. Explain why they're different.
4. Acceleration
A skater slows from 6 m/s to 2 m/s in 4 seconds. Find the acceleration. Is it positive or negative — and does that mean the skater is speeding up or slowing down? Explain.
5. Position-Time Graphs
Sketch a position-time graph for this story: a student walks away from their locker at a steady pace for 10 seconds, stops and talks to a friend for 5 seconds, then walks back to their locker twice as fast as before.
6. Velocity-Time Graphs
A car's velocity increases steadily from 0 to 12 m/s over 6 seconds, then stays constant at 12 m/s for the next 4 seconds. Find (a) the acceleration during the first 6 seconds and (b) the displacement during the last 4 seconds.
Self-Check
Circle your confidence (1 = not confident, 5 = very confident) for each topic:
| Topic | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Distance/Displacement | |||||
| Vectors/Scalars | |||||
| Average Velocity/Speed | |||||
| Acceleration | |||||
| Position-Time Graphs | |||||
| Velocity-Time Graphs |
My weakest topic is: _______________________