Graphing Motion SAMPLE Word Problems
NAME: Ms. Bacic
Nelson pg 38 - Sample Problem #2: What distance does the boat travel if…..
…..a sailboat accelerates uniformly form 6.0 m/s [N] to 8.0 m/s [N] at a rate of 0.50 m/s2 [N].
A: Pictorial Representation & Givens
Sketch, coordinate system, label givens & unknowns, conversions…
Givens:
V1 = 6.0 m/s
V2 = 8.0 m/s
a = 0.5 m/s2
Unknown:
Δt = ?
Δd = ?
Equations:
V2 2 = V1 2 – 2aΔd
Δd = V2 2 - V1 2
2a
OR
a = ΔV / Δt
a = V2 – V1
Δt
Δt = ΔV / a
V2 = 8.0 m/s [N]
V2 – V1 = ΔV
= 2.0 m/s
The question doesn’t ask for time but to graph,
you will need time.
V1 = 6.0 m/s
Δt
B: Physics Representation – Use values found from your calculations. Label & include units on each axis.
Motion diagram, motion graphs, velocity vectors…
30— - -
2--
9— - - - - - - -- -
(m)
(m/s2)
(m/s)
15—
6—
1—
3—
0
[N]
0—
d-t
1 2 3 4 5 6
sec.
v-t 0
a-t
1 2 3 4 5 6
1 2 3 4 5 6
sec.
sec.
C: Word Representation
Describe motion and any assumptions
-
No assumptions needed, object doesn’t start at rest or stop at any point.
- Also, acceleration due to gravity does not apply in this situation.
The sailboat travels 28 m in 4s shown in the d-t graph
The sailboat increases its velocity from 6.0m/s to 8.0m/s in 4 seconds (v-t graph) at a constant acceleration (a-t graph)
D: Mathematical Representation
Complete equations, algebraically isolate, substitutions, final statement
Substituion:
Δd = V2 2 - V1 2
2a
= ( 82 - 62 ) m2/s2
2(0.5 m/s2)
OR
a = V2 – V1
Δt
Δt = ΔV / a
= 2.0 m/s / 0.5 m/s2
= 4s
Δd = 28 m [N]
→
Δd = ½ (V1 + V2 ) Δt
= ½ (6.0m/s + 8.0m/s) (4s)
Δd = 28 m [N]
E: Evaluation
Does the answer have reasonable size, direction and units?
The sailboat travels 28 m [N] in 4s.