QCEVault

Vector calculus — Question 297

Original QCE Vault practice · 6 marks

Q297 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 297 (6 marks)

A particle has r(t)=4cos⁡(2t)i+4sin⁡(2t)j\mathbf r(t)=4\cos(2t)\mathbf i+4\sin(2t)\mathbf j metres. The question diagram shows its circular path and the point at t=π/8t=\pi/8 s.
Question 150 stimulus; see the question for exact data and required construction.
a)
Use vector calculus to prove that its acceleration is directed towards the centre and has magnitude v2/rv^2/r, where v is its constant speed and r is the radius.
[3 marks]
b)
At the marked point, draw and label the velocity and acceleration directions. Give both vectors exactly.
[2 marks]
c)
Explain why constant speed does not imply zero acceleration here.
[1 mark]
Question linkSyllabus coverage

Related questions

  1. Q9 · Original practice · 6 marks
    Original Specialist Mathematics practice question 9: motion in a plane
    Vector calculus
  2. Q32 · Original practice · 7 marks
    Two particles move for t≥0t\ge0 with positions rA(t)=(2t,t),rB(t)=(6−t,4−2t).\mathbf r_A(t)=(2t,t),\qquad\mathbf r_B(t)=(6-t,4-2t).
    Vector calculus
  3. Q34 · Original practice · 6 marks
    A particle follows the path r(t)=(3cos⁡t,2sin⁡t),0≤t≤2π.\mathbf r(t)=(3\cos t,2\sin t),\qquad0\le t\le2\pi.
    Vector calculus
  4. Q36 · Original practice · 6 marks
    A projectile is launched from level ground at 20 m s−120\ \mathrm{m\,s^{-1}} at 45∘45^\circ above the horizontal. Take g=10 m s−2g=10\ \mathrm{m\,s^{-2}} and ignore air resistance.
    Vector calculus