20. Suppose an object moves so that its velocity at time t is described by the...
(10 pts) Suppose an object moves along a line with velocity v(t) = 3+- 18t +24, for 0 st < 5, where t is measured in seconds and velocity have unit of ft/s. (a) Determine when the motion is in the positive direction and when it is in the negative direction. (b) Find the displacement of the object on the interval 0 st 35. (c) Write down an expression for the distance traveled by the object over the interval 0...
(14 pts.) 3. A particle moves along a line so that its velocity at time t is v(t) = + - + - 6 (measured in meters per second). a) Find the displacement of the particle during the time period 1 st 54. b) Find the distance traveled during this time period.
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 in a straight line with the given velocity u(t) = 6 cos (t) (in m/s). Find the displacement and distance traveled over the time interval [0,71). (Give your answers as whole or exact numbers.) displacement: total distance traveled:
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
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.
(1490) Problem 3: A particle's velocity along the x-axis is described by v(t) = A t+B? where t is in seconds, v is in meters per second, A = 0.85 m/s2. and B =-0.64 m/s- 33% Part (c) What is the distance traveled, in meters, by the particle between times t0 = 1.0 s and t1-3.0 s? -3.0 s?
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...
during the time interval (0,1].We wish to estimate the An object moves with velocity v- t+1 displacement of the object during the whole time interval. Calculate the n-1 Trapezoid sum that estimates this displacement. Use a decimal number (rounded to the nearest tenth, if necessary) to answer. Do not use a fraction, and do not use units. during the time interval (0,1].We wish to estimate the An object moves with velocity v- t+1 displacement of the object during the whole...