Net Change: Motion on a Line

Key Questions

• How do you find the velocity of a particle that moves along a line?

  If #p(t)# is the position function, the the velocity function #v(t)# is #p'(t)#.

  Wataru · · Sep 20 2014
• How do you find the total distance traveled by a particle that moves along a line?

  If #p(t)# is the position function of a particle, the distance traveled by the particle from #t=t_1# to #t=t_2# can be found by
  #int_{t_1}^{t_2}|p'(t)|dt#.

  Wataru · · Sep 9 2014

• How do you find the velocity of a particle that moves along a line?
• How do you find the stationary points of a particle that moves along a line?
• How do you find the speed of a particle that moves along a line?
• How do you find the displacement of a particle that moves along a line?
• How do you find the total distance traveled by a particle that moves along a line?
• How do you find the instantaneous velocity for the particle whose position at time #t# is given by #s(t)=3t^2+5t# ?
• How do you find the instantaneous acceleration for the particle whose position at time #t# is given by #s(t)=3t^2+5t# ?
• How do you find the total displacement for the particle whose position at time #t# is given by #s(t)=3t^2-5t# on the interval #0<=t<=2#?
• How many values of t does the particle change direction if a particle moves with acceleration #a(t)=3t^2-2t# and it's initial velocity is 0?
• What is the position of a particle at time #t=2# if a particle moves along the x axis so that at any time #t>0#, the velocity is given by #v(t)=4-6t^2#, and at position #x=7# at #t=1#?
• How do you find the position function #x(t)# if you suppose that the mass in a mass-spring-dashpot system with #m=25#, #c=10# and #k=226# is set in motion with #x(0)=20# and #x'(0)=41#?
• How do you solve the AP Calculus AB 2013 Free Response question #2? http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_calculus_ab.pdf
• What is the farthest apart the particles ever get if the positions of two particles on the s-axis are #s_1=cos(t)# and #s_2=cos(t+pi/4)#?
• An object moves so that at time t its position s is found using #s(t) = 5*cos(t)#. For what values of 't' does the object change direction?
• Question #5def0
• How do you solve 2015 AP Calculus AB Question #1?
• 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?
• A particle is constrained to move in #Q_1#, in a parabolic groove # y = x^2#. It was at O, at t = 0 s. At time t s, its speeds in the directions Ox and Oy are 5 and 12 cm/s, respectively. How do you prove its direction makes #67^o22'49''# with Ox?
• Calculate the work done by a particle under the influence of a force #y^2 hat(i) - x^2hat(j)# along the curve #y=4x^2# from #(0,0)# to #(1,4)#?
• 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?
• Consider a particle moving along the x-axis where x(t) is the position of the particle at time t A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t)=5cos(t). At t=0, its position is x=2?
• The acceleration of a particle at time #t# seconds is given by # a = 6t#. Given that #v=10# when #t=0# and that #x=7# when #t=0# find #x# when #t=2#?