Calculate total displacement and average velocity in a plane when given velocity and time.

1. Lesson 6
Finding Total Displacement and
Average Velocity from
Velocity and Time
Done by Example

2. Example
A canoeist paddles 2.0 m/s [E] for 15 minutes.A canoeist paddles 2.0 m/s [E] for 15 minutes.
She then paddles 3.0 m/s [N] for 20 minutes.She then paddles 3.0 m/s [N] for 20 minutes.
Determine:Determine:
 (a) Total displacement(a) Total displacement
 (b) Average velocity(b) Average velocity
Solution
Δd1 = v1 Δt = 2.0 m/s [E] x (15 min.x 60s/min.)
= 1.8 km [E]
Δd2 = v2 Δt = 3.0 m/s [N] x (20 min.x 60s/min.)
= 3.6 km [N]
The next step is to draw a non-scaled vector
diagram, since the two displacement vectors
are not linear.

3.  The length ofThe length of Δd1 should be
half of the length of Δd2. And
this is what has been drawn
(do by eye no need to
measure).
 If we do the calc. we find
that |ΔdT| = 4.0 km. The
angle is calc. using Tan-1
=(3.6/1.8) = 630
 So, ΔdT = 4.0km [E630
N]
We calc |vav|=|ΔdT |/ ΔtT, get
{4.0km/(35min/(60min/hr))}
= 6.9km/h [E630
N]
N
W E
d 1 = 1 .8 k m
d2=3.6km
d
T=
1.82
+3.62
km

4. Practice Questions
From Nelson TB
Page 65 #9,Page 65 #9,
Page 94 #49, 53Page 94 #49, 53
From McGraw-Hill TB
1.1. A hiker walks at 5.0 km/h [N35E] for 48.0 min.A hiker walks at 5.0 km/h [N35E] for 48.0 min.
He then heads west at 4.5 km/h for 40.0 min.He then heads west at 4.5 km/h for 40.0 min.
Finally he heads 6.0 km [N30W] for an additionalFinally he heads 6.0 km [N30W] for an additional
1.50 hours and arrives at his campsite.1.50 hours and arrives at his campsite.
Determine: a.) Total displacement – a scaledDetermine: a.) Total displacement – a scaled
diagram is required. b.) Average velocity for thediagram is required. b.) Average velocity for the
entire hike.entire hike.
Ans. 9.2 km [N24W] , 3.1 km/h [N24W]

5. Practice Questions
2. A runner runs 15.0 km [N35E] and then
7.5 km [N25W]. Entire trip takes 2.0 h.
Determine: a.) Total displacement b.)
Average velocity
Ans. 20.0km [N16E], 9.9 km/h [N16E]

6. Practice Questions
2. A runner runs 15.0 km [N35E] and then
7.5 km [N25W]. Entire trip takes 2.0 h.
Determine: a.) Total displacement b.)
Average velocity
Ans. 20.0km [N16E], 9.9 km/h [N16E]