For t ≥ 0, a particle moves along the x-axis. The velocity of the particle at time t is given by ...
please answer all questions For 1 2 0, a particle moves along the r-axis. The velocity of the particle at time t is given by r(t)-1 + 2sin(2) Theparticle is atposition x = 2 attimet=4. (a) At time t-4, is the particle speeding up or slowing down? (b) Find all times t in the interval o<t<3 when the particle changes direction. Justify your answer. (c) Find the position of the particle at time t 0. (d) Find the total distance...
1095 (1999AB, Calculator). A particle moves along the y-axis with velocity given by v(t) = t sin(t?) for t 0. a) In which direction (up or down) is the particle moving at time t = 1.5? Why? b) Find the acceleration of the particle at time t = 1.5. Is the velocity of the particle increasing at t = 1.5? c) Given that y(t) is the position of the particle at time t and that y(0) = 3, find y(2)....
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
A particle moves along the x-axis so that its velocity at any time t/geq0 is given by v(t) = 1 - sin(2t). (a) Determine the expression for acceleration at any time t. (b) Find all values t, 0 <t<2, for which the particle is at rest. (c) Determine the expression for the position Jf the particle at any timet if x(0) = 0.
A particle moves along the x-axis with velocity given by v(t) = 32 – 1 for time t > 0. If the particle is at position x = 5 at time t = 0, what is the position of the particle at timet 1?
A particle starts at x=0 and moves along the x-axis with velocity v(t)=2t+1 for time t is less than or equal to 0. Where is the particle at t=4?
A particle moves along a straight line and its position at time t is given by s(t)= 2t^3 - 21 t^2 + 60 t where s is measured in feet and t in seconds.a) Find the velocity (in ft/sec) of the particle at time t=0:The particle stops moving (i.e. is in a rest) twice, once when t=A and again when t=B where A < B.b) A isc) B isd)What is the position of the particle at time 14?e)Finally, what is...
Problem #1 (35 Points) Given The velocity of a particle as it moves along a straight line is given by v (-12+36t-6t2) ft/s, where t is in seconds. At the initial condition ( 0), so 2 ft. Find a) The acceleration of the particle as a function of time. b) The acceleration of the particle when -6 seconds. c) The position of the particle as a function of time. d) The position of the particle when -6 seconds. e) The...
The position of a particle as it moves along the x axis is given for t > 0 by x = (t^3-3t^2+6t)m. Where is the particle when it achieves its minimum speed (after t = 0)?
A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs = 6.0 m/s. (a) what is the coordinate of the particle at t = 5.0 s? (b) what is the velocity of the particle at t = 5.0 s? (c) what is the acceleration of the particle...