Vocabulary & Concepts
Define scalar and vector in one dimension. Give one example of each.
Scalar = magnitude only (e.g., time, distance, speed). Vector = magnitude + direction (sign in 1D) (e.g., displacement, velocity, acceleration).
In GUESS, what does the “G” stand for and what should you list?
G = Given, list knowns with units/signs.
Maria sprinted for 5.0 s with an acceleration of 2.0 m/s², reaching 14.0 m/s. What was her initial velocity?
v₀=4.0 m/s
A toy car travels 30 m in 3.5 s from rest. Find its acceleration.
a≈4.90 m/s²
A scooter at 2.5 m/s² from rest covers 50 m. How long was it accelerating?
t≈6.32 s
Distance vs. displacement: if you walk +6 m, –3 m, +2 m, what is distance and displacement?
Distance = 6 + 3 + 2 = 11 m.
Displacement = (+6) + (−3) + (+2) = +5 m (to + direction).
Which kinematic equation should you choose if time is not given? Why?
Use v² = v₀² + 2aΔx when time is not given.
A catapult launches a boulder at 10 m/s, rolling 18 m with 2 m/s². What is its final velocity?
v=13.1 m/s
Emily’s robot covers 62.5 m in 5.0 s from rest. Find its acceleration.
a=5.00 m/s²
The Hindenburg fell for 12 s under gravity. How far did it fall?
x≈705.6 m
Why must vectors always include a sign or direction in 1D?
Because direction matters physically; the sign tells “which way” along the line. Without it, you only know a magnitude.
A car accelerates from rest at 3 m/s² for 5 s. Identify the unknown, equation, and knowns (don’t solve).
G: v₀=0, a=3.0, t=5.0. U: v. E: v=v₀+at.
Apollo 11 accelerates from rest at 15 m/s² for 8 s. What is its velocity?
v=120 m/s
A superhero dashes from 5 m/s to 15 m/s over 20 m. What’s the acceleration?
a=5.00 m/s²
Ethan’s prototype car accelerates 3.0 m/s², traveling 67.5 m. How much time passed?
t≈6.71 s
A velocity–time graph shows +2 m/s for 3 s, then –1 m/s for 2 s. Find displacement and total distance.
Displacement = (+2)(3) + (−1)(2) = +4 m.
Total distance = |+2|·3 + |−1|·2 = 8 m.
What makes the GUESS method helpful compared to just plugging numbers?
GUESS organizes information, reduces errors.
A roller coaster starts at 12 m/s, accelerates 3 m/s² over 22 m. What is its final speed?
v≈16.6 m/s
A rocket capsule slows from 100 m/s to 20 m/s across 300 m. What’s the acceleration?
a=−16.0 m/s²
A rocket accelerates at 15 m/s² for 8 s. How far did it travel?
x=480 m
Explain why negative acceleration does not always mean “slowing down.” Give an example.
“Speeding up/slowing down” depends on relative signs of v and a.
For each of the 5 kinematic equations, name a real-world example where that equation is most useful.
v=v₀+at (sprints),
x=x₀+v₀t+½at² (fall),
v²=v₀²+2aΔx (braking),
v̄=(v+v₀)/2 (avg vel.),
Δx=v̄t (distance).
A sandbag falls 75 m under 9.8 m/s². What is its velocity when it hits?
v≈38.3 m/s downward
A train decelerates from 15 m/s to rest at –2.5 m/s². How far does it travel before stopping?
Δx=45.0 m
A Great Wall signal rocket accelerates 25 m/s² for 4 s. How high did it rise?
x=200 m