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Federal (FBISE) · Chapter test · Free

2nd Year Mathematics Chapter 5 Test05: Kinematics of Motion in a Straight Line

21 marks · 40 minutes · 14 questions. Covers: 05: Kinematics of Motion in a Straight Line.

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2nd Year Mathematics Chapter 5 Test

2nd Year · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 21Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 9 × 1 = 9)

  1. Which of the following quantities is a vector?
    1. Charge
    2. Mass
    3. Momentum
    4. Time
  2. Which of following can be used to determine the magnitude of velocity?
    1. Area under acceleration–time graph
    2. Area under velocity-time graph
    3. Gradient of an acceleration–time graph
    4. Gradient of a velocity–time graph
  3. A car travels 100 km. The journey takes two hours. The highest speed of the car is 80 km/h, and the lowest speed 40 km/h. What is the average speed for the journey?
    1. 40 km/h
    2. 50 km/h
    3. 60 km/h
    4. 120 km/h
  4. A heavy object is released near the surface of earth and falls freely. Air resistance can be ignored. Which statement about the acceleration of the object due to gravity is correct?
    1. The acceleration depends on mass of the object.
    2. The acceleration depends on volume of the object.
    3. The acceleration is constant.
    4. The acceleration is initially zero and increases as the object falls.
  5. Which of following is scalar quantity?
    1. Displacement
    2. Weight
    3. Force
    4. Work
  6. The winner of 400 metre race must have the greatest:
    1. acceleration
    2. average speed
    3. instantaneous speed
    4. maximum speed
  7. Which person is experiencing an acceleration?
    1. A driver of a car that is braking to stop at traffic light.
    2. A passenger in a train that is stationary in a railway station.
    3. A shopper in a large store ascending an escalator at a uniform speed.
    4. A skydiver that is falling at a constant speed towards the Earth.
  8. A child is standing on the platform of station. A train travelling at 30 m/s takes 3.0 s to pass the child. What is length of train?
    1. 10 m
    2. 27 m
    3. 30 m
    4. 90 m
  9. A car travels 6.0 km along a main road in 6.0 minutes. It then travels 2 km along minor road in 6.0 minutes. Which calculate of average speed for the whole journey is correct?
    1. 8.012.0=0.67kmmin\frac{8.0}{12.0}=0.67\frac{km}{min}
    2. 12.08.0=1.5kmmin\frac{12.0}{8.0}=1.5\frac{km}{min}
    3. 8.0+12.0=20kmmin8.0 + 12.0 = 20\frac{km}{min}
    4. 8.0×12.0=96kmmin8.0 \times 12.0 = 96\frac{km}{min}

Q2. Short questions (Attempt all · 2 × 2 = 4)

  1. Find the derivative of the vector function at f(t)=2t2i^+8j−1t3k^at t=5. f(t) = 2t^2\hat{i} + 8j - \frac{1}{t^3}\hat{k} \quad \text{at } t = 5.
  2. Find the domain of r(t)=ln⁡∣t−1∣ t^+et j^+t k^ r(t) = \ln|t - 1| \, \hat{t} + e^t \, \hat{j} + \sqrt{t} \, \hat{k}

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Find the velocity and acceleration of the function at t = 0.r(t)=(3t+1)i+3tj+t2k r(t) = (3t + 1)i + \sqrt{3}tj + t^2k
  2. Find the scalar valued function in terms of the magnitude.r(t)=(t2)i+(t2+16t2)j−2tkr(t) = \left( \frac{t}{\sqrt{2}} \right) i + \left( \frac{t}{\sqrt{2}} + 16t^2 \right) j - 2tk
  3. A particle P moves along the x-axis in a straight line so that, at time t seconds, the velocity of P is v m/s, where v={10t−2t2,0≤t≤4,−432t2,t>6.m/s, \text{ where } v = \begin{cases} 10t - 2t^2, & 0 \leq t \leq 4, \\ -\frac{432}{t^2}, & t > 6. \end{cases} At t=0 t = 0 , P is at the origin O. Find the displacement of P from O when: (1) t=6s t = 6s , (2) t=10s t = 10s .