SPM Mathematics Trial 2021 (Selangor), Paper 2 (Question 11 & 12)

Question 12:
The speed-time graph in Diagram 7 shows the motion of an object for a period of t seconds.

(a) Calculate
(i) uniform speed,
(ii) the rate of change of speed, in ms^-2, of the object in the first 5 seconds.
[3 marks]

(b) Find the value of t, if the distance travelled by the object for the first 5 seconds if half the distance travelled at uniform speed. [3 marks]


Solution:
(a)(i)
Laju seragam = 10 ms^-1

(a)(ii)

$\begin{array}{l}\text{The rate of change of speed in the first 5 seconds}\\ =\text{gradient of the graph}\\ =\frac{10-6}{5-0}\\ =\frac{4}{5}\\ =0.8{\text{ ms}}^{\text{-2}}\end{array}$


(b)

$\begin{array}{l}\text{For speed-time graph, distance travelled is area under the graph}\text{.}\\ \text{Given area of trapezium}=\frac{1}{2}\times \text{area of rectangle}\\ \frac{1}{2}\times \left(6+10\right)\times 5=\frac{1}{2}\times \left(t-5\right)\times 10\\ 80=10t-50\\ 10t=130\\ t=13\end{array}$