Page 21 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4 Mathematics Chapter 7 Graphs of Motion

3. Solve problems involving speed-time graphs
Speed Positive gradient represents
acceleration (Speed keeps
on increasing) Example 12
O Time The diagram below shows the speed-time graph
Zero for the movement of two particles P and Q in a
gradient
Speed period of 30 seconds.
Interpretation represents Speed (m s )
–1
of speed-time zero
graph acceleration 20 B
©PAN ASIA PUBLICATIONS
O Time (Uniform
speed) 16 C
Speed u D
Negative gradient
represents deceleration A
O Time (Speed keeps on decreasing) O 18 F 30 E Time (s)
Example 11 Graph AB represents the movement of particle P
whereas graph CDE represents the movement of
The speed-time graph below shows Maria’s run in particle Q.
a sports practice. (a) Determine the value of u.
Speed (m s ) (b) By using the value of u obtained in (a), find
–1
10 A B the acceleration of particle Q in the first
CHAP. 18 seconds.
7 (c) Calculate the difference between the distance
travelled by particles P and Q in the period of
30 seconds.
C
O Time (s)
5 15 18 Solution:
(a) Find the acceleration, in m s , for the (a) Gradient AD = gradient AB
–2
(i) first 5 s, u = 20
(ii) duration of time from 5 s until 15 s, 18 30
(iii) last 3 s. u = 20 × 18
(b) Hence, describe Maria’s run in the period of 30
18 s. = 12
(b) Acceleration = gradient CD
Solution: = – 16 – 12
(a) (i) Acceleration = gradient OA 4 18
= 10 = – 18
5
2
= 2 m s –2 = – m s –2
(ii) Acceleration = gradient AB 9
= 0 m s –2 (c) Distance travelled by particle P
(iii) Acceleration = gradient BC = area of triangle ABE
1
= – 10 = 2 × 30 × 20
18 – 15 = 300 m
10
= – m s –2 Distance travelled by particle Q
3
BRILLIANT Tips = area of trapezium ACDF + area of triangle
DEF
1
Negative acceleration is known as deceleration. = 1 × (16 + 12) × 18 + × 12 × 12
2 2
= 252 + 72
(b) For the first 5 s, Maria ran from 0 m s until
–1
10 m s with acceleration 2 m s . After = 324 m
–1
–2
that, she ran with speed 10 m s for 10 s Difference between the distance travelled by
–1
particles P and Q = 324 – 300
and decreased her speed with deceleration = 24 m
1
3 m s until finally stopped.
–2
3 Try question 6 in Formative Zone 7.2
Try question 5 in Formative Zone 7.2
144 7.2.3 7.2.4

ENG07 Spotlight Matematik F4.indd 144 16/03/2021 8:58 AM