Net Change: Motion on a Line - Page 2

Questions
  • A particle moves along a horizontal line according to the position function #s(t)=t^3-12t^2+36t#, where t is measured in seconds and s is in metres. How do you find the total distance travelled during the first 8 seconds?
  • The movement of a certain glacier can be modelled by d(t) = 0.01t^2 + 0.5t, where d is the distance in metres, that a stake on the glacier has moved, relative to a fixed position, t days after the first measurement was made. Question?
  • Find the value of the line integral. F · dr (Hint: If F is conservative, the integration may be easier on an alternative path.) (2x − 8y + 6) dx − (8x + y − 6) dy?
  • Find the value of the line integral.F · dr (Hint: If F is conservative, the integration may be easier on an alternative path.) F(x,y) = ye^xyi + xe^xyj (a) r1(t) = ti − (t − 8)j, 0 ≤ t ≤ 8 ?
  • What is the arc length of #r(t) = (t, t, t)# in the interval #[1,5]#?
  • What is the arc length of #r(t) = (t^2, 1-t^2, -t)# in the interval #[0,1]#?
  • The velocity of a particle moving along the x-axis is given by v(t) = tsin(t^2). Find the total distance traveled from t = 0 to t = 3. A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 3.0 ?
  • How to find the distance travelled using calculus?
  • A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential component of its acceleration are equal. If its speed at t = 0 is #v_o#, the time taken to complete the first revolution is?
  • A pinecone falls from a tree. The pinecone's height #y# (in feet) after #t# seconds can be modeled by #64-16t^2#. After how many seconds does the pinecone hit the ground?
  • Why does a Gaussian wave packet take on the minimum value of the Heisenberg Uncertainty Principle?
  • A particle travels the circumference of the equation x^2 + y^2 = 1 counterclockwise. At what points in the circle does the ordinate(y) decrease with the same speed that the abscissa(x) grows? Use derivates
  • The acceleration of a particle moving along the x-axis is given by a = #2x^3-10x#. a) if u = 3 show that the particle oscillates within the interval #-1<=x<=1# b) Why is it not simple harmonic motion c) if u=6 describe the motion?
  • Find the value of the line integral. F · dr C (Hint: If F is conservative, the integration may be easier on an alternative path.) F(x, y) = yi − xj?
  • Find the value of the line integral F · dr C (Hint: If F is conservative, the integration may be easier on an alternative path.) (x2 + y2)dx + 2xy dy?