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13. Fully describe the motion shown in each graph. Refer to direction,
displacement, velocity, and acceleration and include the words positive,
negative, increasing, and decreasing.
(a)
(b) s(t)
s(t)
s
s
t
t
14. Communication: A car screeches to a sudden stop at a stop sign.
Describe the car’s distance from the stop sign, velocity, and acceleration
as positive, negative, large, small, increasing, and decreasing.
Sketch graphs for this situation that show
(a) position versus time
(b) velocity versus time
(c) acceleration versus time
15. Thinking, Inquiry, Problem Solving: A space probe on the surface of Mars
conducts several experiments. It launches a small weight and tracks the
weight’s motion using a motion detector. The table shows the data that the
probe collected.
Time (s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Height (m) 0.50 5.01 8.54 11.09 12.66 13.25 12.86 11.49 9.14 5.81 1.50
(a) Determine the initial velocity of the weight.
(b) Determine the velocity at which the weight falls to the surface of Mars.
(c) Determine the force of gravity on Mars.
(d) If the probe launched the same weight on Earth, with the same initial
velocity, how long would the weight take to return to the ground?
10
8
6
4
2
–2 –1
–2
–4
–6
–8
–10
y
1
2
3
4
5 6
16. A particle moves on a vertical line. Its position, s, in metres at t seconds is
given by s(t) t 3 9t 2 24t, t ≥ 0.
(a) Determine the velocity and acceleration functions.
(b) When is the particle moving up? down?
(c) Find the distance the particle travels between t 0 and t 6.
(d) Graph the position, velocity, and acceleration functions for the interval
0 ≤ t ≤ 6.
x
(e) When is the particle speeding up? slowing down?
17. Check Your Understanding: The graphs of f , f ′, and f ′′ are shown on
the left. Which graphs correspond to which functions? Explain your
reasoning.
A function and its derivatives
254 CHAPTER 3 RATES OF CHANGE IN POLYNOMIAL FUNCTION MODELS