6.3 SPM Practice (Long Questions)


Question 9:
Diagram below shows the speed-time graph for the movement of an object for a period of 34 seconds.


(a) State the duration of time, in seconds, for which the object moves with uniform speed.
(b) Calculate the rate of change of speed, in ms-2, of the object for the first 8 seconds.
(c) Calculate the value of u, if the average of speed of the object for the last 26 seconds is 6 ms-1.

Solution:
(a) Duration of time = 26s – 20s = 6s

(b)Rate of change of speed for the first 8 seconds=10608=48=12 ms2

(c)Speed=DistanceTime(12×12×(6+u))+(6×u)+(12×8×u)26=6  36+6u+6u+4u=156   16u=120   u=7.5 ms1




Question 10 (6 marks):
Diagram 11 shows the speed-time graph for the movement of a particle for a period of t seconds.

Diagram 11

(a) State the uniform speed, in ms-1, of the particle.

(b)
 Calculate the rate of change of speed, in ms-2, of the particle in the first 4 seconds.

(c)
 Calculate the value of t, if the distance travelled in the first 4 seconds is half of the distance travelled from the 6th second to the tth second.


Solution:
(a)
 Uniform speed of the particle = 12 ms-1

(b)
Rate of change of speed of particle=124=3 ms2

(c)
Distance travelled in the first 4 seconds =12(Distance travelled from the 6th second to tth second)12×4×12=12[12(12+20)(t6)]24=12[16(t6)]24=8(t6)24=8t483=t6t=9