3.02g Non-uniform acceleration in two dimensions Quiz: OCR Maths, Unit 17

The 20 questions

1. How do you calculate the velocity vector from a given 2D displacement vector r(t)?

   • Integrate r
   • Integrate v
   • Differentiate x
   • Differentiate r

2. How do you calculate the displacement vector from a given 2D velocity vector v(t)?

   • Differentiate v
   • Integrate v
   • Differentiate r
   • Integrate a

3. How do you calculate the acceleration vector from a given 2D velocity vector v(t)?

   • Integrate a
   • Differentiate v
   • Differentiate r
   • Integrate v

4. If displacement is r = (t³ i + 2t j) m, what is the velocity vector v?

   • 3t² i + 2 j
   • 6t i
   • 3t² i + 2t j
   • t² i + 2 j

5. If velocity is v = (4t i + 3 j) m/s, what is the acceleration vector a?

   • 4 i
   • 2t² i
   • 4t i + 3 j
   • 4 i + 3 j

6. What is the speed of a particle when its velocity vector is v = (3 i - 4 j) m/s?

   • 1 m/s
   • 5 m/s
   • 7 m/s
   • 25 m/s

7. If acceleration is a = (6t i + 2 j) m/s² and v(0) = 0, what is v(t)?

   • 3t² i + 2t j
   • 3t² i + 2 j
   • 6 i
   • 6t² i + 2t j

8. In 2D vector notation, how is acceleration due to gravity represented standardly downwards?

   • g j
   • g i
   • (-g i - g j)
   • -g j

9. If displacement is r = (3t i + 4t j) m, what is the distance from origin at t = 2 s?

   • 10 m
   • 14 m
   • 7 m
   • 20 m

10. If velocity is v = (2t i - 6t² j) m/s, what is the acceleration vector at t = 1 s?

    • 2 i - 18 j
    • 2 i - 6 j
    • i - 12 j
    • 2 i - 12 j

11. If acceleration is a = 3 i m/s² and v(0) = 8 j m/s, find speed at t = 2 s.

    • 8 m/s
    • 10 m/s
    • 6 m/s
    • 14 m/s

12. If displacement is r = (t³ i + (12t - 3t²) j) m, when is vertical velocity zero?

    • 2 s
    • 4 s
    • 3 s
    • 1 s

13. What mathematical operation on a 2D velocity vector yields the scalar speed of a particle?

    • Vector magnitude
    • Vector addition
    • Scalar differentiation
    • Dot product

14. What type of constant must be added when integrating a 2D vector expression indefinitely?

    • Unit vector
    • Scalar constant
    • Zero scalar
    • Constant vector

15. If v = (6t i + 4 j) m/s and r(0) = (i + 2 j) m, find displacement r(1).

    • 4 i + 6 j
    • 3 i + 4 j
    • 3 i + 6 j
    • 4 i + 4 j

16. If displacement is r = ((t² - 4t) i + 5t j) m, when is motion parallel to the j-axis?

    • 5 s
    • 0 s
    • 4 s
    • 2 s

17. If displacement is r = (2t² i + (t³ - 3t) j) m, when is motion parallel to the i-axis?

    • 1 s
    • 0 s
    • 3 s
    • 2 s

18. If acceleration a = (3 i + 8t j) m/s² and v(0) = 0, find speed at t = 1 s.

    • 7 m/s
    • 25 m/s
    • 11 m/s
    • 5 m/s

19. If displacement is r = (4 cos t i + 4 sin t j) m, find the acceleration magnitude.

    • 0 m/s²
    • 4 m/s²
    • 8 m/s²
    • 16 m/s²

20. In column vector notation, how is the displacement vector r obtained from velocity vector v?

    • Integrate velocity vector
    • Differentiate position vector
    • Differentiate velocity vector
    • Integrate acceleration vector

Related quizzes

• Methods of proof Quiz · 1.01 · 20 questions
• Indices and surds Quiz · 1.02a · 20 questions
• Straight lines and circles Quiz · 1.03a · 20 questions
• Binomial expansion Quiz · 1.04a · 20 questions
• Trigonometric functions and triangles Quiz · 1.05a · 20 questions
• Exponential functions Quiz · 1.06a · 20 questions
• Gradients and second derivatives Quiz · 1.07a · 20 questions
• Fundamental theorem of calculus Quiz · 1.08a · 20 questions
• Locating and approximating roots Quiz · 1.09a · 20 questions
• Vectors in two and three dimensions Quiz · 1.10a · 20 questions