Mechanics : Distance v's' time graphs

1
Mechanics Distance v.s. time graphs

• By the end of this presentation, you should be
  able to
• Plot and sketch distance / time graphs for moving
  objects.
• Use these graphs to describe the motion at any
  time during the objects journey.
• Determine the speed of an object from a distance
  time graph.

2
Use graph paper to plot the distance/ time graph
for the car described.

• At the beginning of the experiment (t0s) the car
  is stationary and point X.
• Once it begins to move it covers 5m in every
  second for the first 10 seconds of the
  experiment.
• It then slows down. It is recorded that the car
  only covers 30m in the next 10 seconds.
• The brakes are then suddenly depressed and the
  car comes to a complete and sudden stop.
• Plot a distance v.s. time graph for 0 to 30
  seconds of time.

3
The graph

• Distance (m)

X
X
X
X
X
X
X
Time (s)
4
What information can we get from this graph?

• 1. What is the speed of the car in each of the
  10s periods?
• 2. How far does the car travel in the first 2s of
  motion?
• 3. How far does it travel in the next 2s of
  motion?
• 4. In which of the 10s periods is the speed
  constant?

d (m)
t (s)
1a. From 0s to 10s speed 50/10 5m/s 1b. From
10s to 20s speed 30/10 3m/s 1c. From 20s to
30s speed 0/10 0m/s
5
What information can we get from this graph?
d (m)
Can you see a link between the calculated values
of speed and the gradient of the line in each
stage?
0m/s
3m/s
5m/s
The higher the speed, the steeper the gradient.
In fact, the gradient the speed
t (s)
6
What information can we get from this graph?

• 2. How far does the car travel in the first 2s of
  motion?
• The car travels a total of 5 x 2 10m in the
  first 2s.
• 3. How far does it travel in the next 2s of
  motion?
• The car travels the same distance in the next 2s
  10m

d (m)
0m/s
3m/s
5m/s
t (s)
7
What information can we get from this graph?

• 4. In which of the 10s periods is the speed
  constant?

d (m)
t (s)
The car travels at a constant speed of 5m/s in
the first 10s, then at a constant speed of 3m/s
in the next 10s. The car is stationary in the
final 10s.
8
DISTANCE /TIME GRAPHS SUMMARY

• Speed distance / time (measured in m/s)
• A straight line means the speed is constant.
• A constant speed (a straight line) means the
  distance is changing by the same amount every
  second.

d distance covered in metres (m) s speed or
velocity in metres per second (m/s) t time in
seconds (s)
9
Sketching graphs for other objects

• How do you think the distance time graphs for the
  following objects will look?
• A rocket.
• A parachutist.
• A wind up toy.
• A balloon racer.