10 questions · Form 5 Additional Mathematics Bab 8: Kinematics of Linear Motion
What is the condition for a particle to be instantaneously at rest?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the condition for a particle to be instantaneously at rest?
Answer: A
A particle is at rest when its velocity v is equal to 0.
2. Find the acceleration of a particle at t = 2 s if its velocity is v = 2t³ - 5t.
Answer: A
a = dv/dt = 6t² - 5. At t = 2: a = 6(2)² - 5 = 24 - 5 = 19 ms⁻².
3. A particle moves such that its velocity is v = 4 - 2t. What is the total distance traveled from t = 0 to t = 3 s?
Answer: A
Rest point v = 0 => 4 - 2t = 0 => t = 2 s. s = ∫ (4 - 2t) dt = 4t - t². At t = 0: s = 0. At t = 2: s = 4(2) - (2)² = 4 m. At t = 3: s = 4(3) - (3)² = 3 m. Distance = |4 - 0| + |3 - 4| = 4 + 1 = 5 m.
4. Which mathematical operation is used to find displacement s from velocity v?
Answer: A
Since v = ds/dt, integrating v gives displacement s = ∫ v dt.
5. Find the maximum velocity of a particle whose velocity function is v = 12t - 3t².
Answer: A
Maximum velocity occurs when a = dv/dt = 0 => 12 - 6t = 0 => t = 2. Substitute t = 2 into v: v = 12(2) - 3(2)² = 24 - 12 = 12 ms⁻¹.
6. Given acceleration a = 4t - 8 and the initial velocity is 3 ms⁻¹, find the velocity function v(t).
Answer: A
v = ∫ (4t - 8) dt = 2t² - 8t + c. Since initial velocity v(0) = 3, c = 3. Thus, v = 2t² - 8t + 3.
7. Given v = t² - 4t, find the displacement s in the first 3 seconds assuming s = 0 when t = 0.
Answer: A
s = ∫ (t² - 4t) dt = [t³/3 - 2t²] from 0 to 3 = (273 - 2(9)) - 0 = 9 - 18 = -9 m.
8. If displacement s = -15 m, what does this indicate about the position of the particle?
Answer: A
Negative displacement means position is to the left or negative side of the reference origin O.
9. What is the difference between displacement and total distance?
Answer: A
Displacement measures net change in position (vector), whereas total distance sums up all physical movement along the path (scalar).
10. An object has a displacement function s = t³ - 6t² + 9t. Find its initial velocity.
Answer: A
Velocity v = ds/dt = 3t² - 12t + 9. Initial velocity occurs at t = 0: v = 3(0)² - 12(0) + 9 = 9 ms⁻¹.