Graphical Problem Solving and Rockets
So you want to be a world class graphing problem solver? You just want to pass physics? Not to worry! Try
following these steps.
Step 1: Setup the axis for your three graphs one over the other with x vs t (Position vs Time) at the top,
v vs t (Velocity vs Time) in the middle, and a vs t (Acceleration vs Time) on the bottom.
Step 2: Start with the graph that you have the most information about. Plot this graph first (if it hasn’t
already been plotted for you.)
Step 3: It is always easier to go down than up, so examine the slope of your starting graph and plot this
slope on the graph below. For example, the slope of the v vs t graph is acceleration.
Step 4: If it is necessary to go up, look at the area under the curve of your starting graph, and plot the graph
above. For example, the area under the v vs t graph is displacement.
Now you try it!
1. At time t = 0, and at position x = 0, you are stopped at a red light in your car. After waiting 3.0 seconds
for a light change, you accelerate forward (+ direction) gaining 4.0 m/s of speed every second for 6.0
seconds. Next you coast at constant velocity for the next 4.0 seconds. Finally you apply the brakes, and
experience an acceleration of -8.0 m/s2 until you come to rest. Fill in the three motion graphs. Use color!
x vs t
Question 2: At
what distance from
the starting point
does your car
come to rest?
x (m)
0
Area
v vs t
t (s)
Question 1: At
what time does
your car come to
rest?
v (m/s)
Slope
0
4
8
12
a vs t
16
t (s)
a (m/s2)
0
t (s)
1
2. A toy rocket leaves the ground at t = 0 and x = 0, and accelerates upward (in the positive direction) at 6.0
m/s2 for 5.0 s. At t = 5.0 s the fuel runs out and the rocket is in free fall (let g = 10 m/s2)* until its downward
speed gets to 20 m/s (what is its velocity?) At the instant the downward speed reaches 20 m/s a drogue
chute is deployed and the rocket fall the remaining distance to the ground with a constant downward speed
of 20 m/s. (What is the velocity for this part?)
A) Sketch in the v vs t graph only.
v vs t
v
+30
(m/s)
+20
+10
0
2
4
6
8
9
10
12
14
16
18
20
22
t (s)
-10
-20
-30
B) What is the rocket’s maximum velocity?
C) When does the rocket reach its highest point above the ground? (Do you think it is at 5.0 s? Look again!)
D) What is the rocket’s highest distance above the ground? (You don’t need to do the other graphs, but you
do need the graphing ideas from page 1.)
E) At what time does the rocket hit the ground? This is tougher: it occurs when the total area is…what?
Hint: area below the t axis is negative!
*Let the magnitude of the free fall acceleration due to gravity be g = 10 m/s2 for simplicity. Should g be positive or negative in
this problem? (Note: it should be negative: the rocket gains 10 m/s of velocity in the downward direction every second.)
2