A particle moves along the x-axis with velocity given by v(t) = 32 – 1 for...
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.
For timet > 0, the acceleration of a particle moving along the x-axis is given by a (t) = cost+t. At time t = 0, the velocity of the particle is 8 and the position of the particle is 0. What is the position of the particle at time t = ?
For t ≥ 0, a particle moves along the x-axis. The velocity of the particle at time t is given by v(t)=1+2sin(t^2/2). The particle is at x=2 at time t=4. a)Find position of particle at t=0 b)Find the total distance the particle travels from time t=0 to time t=3
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...
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)....
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?
EX #1: For t > 0, a particle moves along a curve so that its position at time t is (x(t), y(t)), where x(t) = 4t and = 1 - 2t. Find the time t at which the speed of the particle is 5.
Int The velocity of a particle along a path is given by v(t)= fort > 0.6 points each) a. Find the acceleration function of the particle along this path. t b. Find the position function of the particle given that its position at t=1 is 5.
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...
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)?