Examples of
Displacement vs. Time Graphs
http://www.stmary.ws/highschool/
physics/home/animations3/motion
_graphs2.html
Distance vs. Displacement
A leprechaun, searching for his Pot o’ Gold, scurries 50 m
North in 10 s. With no luck in finding the gold, he decides
to run 100 m West, taking him 15 s. Off in the distance, he
sees a double rainbow (OMG! All the way!). Scampering to the end of
the rainbow 250 m East, he finds his gold 20 s later.
a) What is the total distance the leprechaun travels?
b) What is the total displacement the leprechaun travels?
c) Draw a distance v. time graph
d) What is the velocity of the leprechaun from 0 – 10 s?
e) What is the velocity of the leprechaun from 10 – 25 s?
f) What is the velocity of the leprechaun from 25 – 45 s?
g) What is the average velocity of the leprechaun?
Answers
a) Distance = 100 m + 50 m + 250 m = 400 m
b) Displacement (y-axis) = 50 m North
Displacement (x-axis) = 250 m – 100 m = 150 m East
Displacement (resultant magnitude) = a2 + b2 = c2
502 + 1502 = c2
Displacement (resultant) = rad(25 000) = c = 158.1 m
Displacement (direction) =
tanθ = opp/adj
θ = tan-1(150/50)
θ = 71.6° East of North
Answers (continued)
c)
d
400
300
200
100
0
5
10
15
20
25
30
35
40
45
t
Answers (continued)
d) Velocity = displacement/time
Velocity = 50 m/10 s = 5 m/s North
e) Velocity = 100 m/15 s = 6.67 m/s West
f) Velocity = 250 m/20 s = 12.5 m/s East
g) v = distance/time = 400 m/45 s = 8.89 m/s
Velocity
 A shopping cart is at rest at the top of a hill. A
slight wind pushes the cart, causing it to start
to roll down the hill with an acceleration of
3.2 m/s2.
a) How fast is the shopping cart moving after it
has travelled a distance of 128.7 m?
b) How much time did it take for the cart to
reach 128.7 m?
c) What would be the velocity at 257.4 m?
d) How long does is take to reach 257.4 m?
Answers
a) Givens: vi = 0.0 m/s; a = 3.2 m/s2; d = 128.7 m
Unknown: vf = ???
Formula: vf2 = vi2 + 2ad
Substitute with units:
vf2 = 0 m/s + 2*(3.2 m/s2)*(128.7 m)
vf2 = 823.68 m2/s2
vf = 28.7 m/s
The “*” indicates multiplication
Answers (continued)
b) Givens: vi = 0.0 m/s; a = 3.2 m/s2; d = 128.7 m
Unknown: t = ???
Formula: d = vit + ½at2
Substitute with units:
128.7 m = (0 m/s)t + ½(3.2 m/s2)t2
128.7 m = (1.6 m/s2)t2
t = rad(80.4375 s2)
t = 9.0 s
Answers (continued)
c) Givens: vi = 0 m/s; a = 3.2 m/s2; d = 257.4 m
Unknown: vf = ???
Formula: vf2 = vi2 + 2ad
Substitute with units:
vf2 = 0 m/s + 2*(3.2 m/s2)*(257.4 m)
vf2 = 1647.36 m2/s2
vf = 40.6 m/s
Answers (continued)
d) Givens: vi = 0.0 m/s; a = 3.2 m/s2; d = 257.4 m
Unknown: t = ???
Formula: d = vit + ½at2
Substitute with units:
257.4 m = (0 m/s)t + ½(3.2 m/s2)t2
257.4 m = (1.6 m/s2)t2
t = rad(160.875 s2)
t = 12.7 s