4) Find the total distance traveled by a particle on the x-axis with acceleration given by...
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5, 0sts 10 v(0) (a) Find the velocity at time t. 2 4t5 2 v(t) m/s (b) Find the distance traveled during the given time interval. 416.6 Need Help? Talk to a Tutor Read It Watch It The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5,...
5) The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. (3 points) a(t) = 5t + 2, v(0) = 6, Osts 4 a) Find the velocity at time t. b) Find the distance traveled during the given time interval. 2) Let F(x) = set? dt. Find an equation of the tangent line to the curve y = F(x) at the point with X-coordinate 2. (2 points)
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...
The acceleration function (in m/s2) and the initial velocity v(o) are given for a particle moving along a line. a(t) = 2t + 2, VO) = -15, Osts 5 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval.
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)....
The acceleration function (in ) and initial velocity for a particle moving along a line is given by (a) Find the velocity (in m/s) of the particle at time . Velocity = meters (b) Find the total distance traveled (in meters) by the particle. Total distance traveled = meters mls2
What is the total distance traveled by the particle? What Velocity vs. Time Graphs Can Tell You Constants A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors...
Find the position function x(t) of a moving particle with the given acceleration a(t), initial position Xo = x(0), and initial velocity vo = v(O). a(t) = 4(t+3)2, v(0) = - 4, x(0) = 2
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
4. The acceleration function of a particle is given by ri" (t) = (2, -2,0). (a) (4 points) Find the position function of the particle if it starts at (2,0,-1) and it's initial velocity is (0,1,0) (b) (2 points) Find the traveled distance of the particle after 2 units of time.