TMUA Applied Mathematics 2 — Questions and Answers
Question 1: A particle moves in a straight line with velocity v = 3t² − 12t + 9 m/s. At what time(s) is the particle momentarily at rest?
- t = 1 s and t = 3 s (Correct answer)
- t = 2 s only
- t = 0 s and t = 4 s
- t = 3 s only
Correct answer: t = 1 s and t = 3 s
Setting v = 0 gives 3t² − 12t + 9 = 0, factoring to 3(t−1)(t−3) = 0, so t = 1 s and t = 3 s.
Question 2: A ball is projected vertically upward with speed 20 m/s from ground level. Taking g = 10 m/s², what is the maximum height reached?
- 10 m
- 20 m (Correct answer)
- 40 m
- 5 m
Correct answer: 20 m
Using v² = u² − 2gs with v = 0 gives s = u²/(2g) = 400/20 = 20 m.
Question 3: A force of 12 N acts on a mass of 3 kg starting from rest. What is the speed after 4 seconds?
- 4 m/s
- 8 m/s
- 16 m/s (Correct answer)
- 12 m/s
Correct answer: 16 m/s
Acceleration a = F/m = 12/3 = 4 m/s², then v = u + at = 0 + 4(4) = 16 m/s.
Question 4: A discrete random variable X has P(X = 1) = 0.3, P(X = 2) = 0.5, P(X = 3) = 0.2. What is E(X)?
- 1.9 (Correct answer)
- 2.0
- 1.8
- 2.1
Correct answer: 1.9
E(X) = 1(0.3) + 2(0.5) + 3(0.2) = 0.3 + 1.0 + 0.6 = 1.9.
Question 5: A uniform beam of length 4 m and weight 200 N is supported at both ends. A 100 N load is placed 1 m from the left end. What is the reaction at the left support?
- 125 N
- 175 N (Correct answer)
- 100 N
- 150 N
Correct answer: 175 N
Taking moments about the right support: R_L × 4 = 200 × 2 + 100 × 3 = 700, so R_L = 175 N.
Question 6: A biased coin shows heads with probability 0.6. If tossed 5 times, what is the probability of exactly 3 heads?
- 0.3456 (Correct answer)
- 0.2304
- 0.3125
- 0.1728
Correct answer: 0.3456
P(X=3) = C(5,3)(0.6)³(0.4)² = 10 × 0.216 × 0.16 = 0.3456.
Question 7: An object undergoes simple harmonic motion with amplitude 3 m and period 2π s. What is the maximum speed?
- 3 m/s (Correct answer)
- 6π m/s
- 3π m/s
- 6 m/s
Correct answer: 3 m/s
ω = 2π/T = 1 rad/s, so v_max = Aω = 3 × 1 = 3 m/s.
TMUA Applied Mathematics 2
A particle moves in a straight line with velocity v = 3t² − 12t + 9 m/s.
At what time(s) is the particle momentarily at rest?