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The given function represents the position of a particle traveling along a horizontal line. s(t) =...
(9 points) The function (t) describes the position of a particle moving along a coordinate line, where ® is in feet and t is in seconds t> 0 8(t) = +"- 8t+ 16, If appropriate, enter answers in radical form. Use inf to represent co. (a) Find the velocity and acceleration functions. u(t): a(t): (b) Find the position, velocity, speed, and acceleration at t=1. Position (ft): Velocity (ft/sec): Speed (ft/sec): Acceleration (ft/sec): (c) At what times is the particle stopped?...
11. Suppose the position function of a particle moving along a straight line is given s(t) = t3 - 3t2 + 8, where s is in meters and t is in seconds. Include units in your responses. (a) How far has the particle traveled in 1 second? (b) What is the velocity of the particle at 1 second? (c) What is the acceleration of the particle at 1 second? (d) is the particle speeding up or slowing down or neither...
(1 point) The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t) = 12 – In(t + 3), t20 36 If appropriate, enter answers using In . Use inf to represent oo. (a) Find the velocity and acceleration functions. u(t): a(t): (b) Find the position, velocity, speed, and acceleration at t = 1. Position (ft): Velocity (ft/sec): Speed (ft/sec): Acceleration (ft/sec2): 000 (c) At what...
Show all work. The function s = f(t) gives the position of a moving object 9) A particle moves according to a law of motion s = f(t) fort > 0 where t is measured in seconds and s in feet. f(t) = 13 - 912 + 150 (a) Find the velocity at time t. v(t) = (b) What is the velocity after 3 seconds ? (3) = (c) When is the particle at rest? (d) When is the particle...
The function s(t) describes the motion of a particle along a line. s(t) - 663 - 8t + 2 (a) Find the velocity function v(t) of the particle at any time t 2 0. v(t) = (b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify...
A particle is travelling along a 1D axis (s-axis) and it's velocity is given as a function of time as, v(t) 3t2-5 in m/s. The initial position of the particle is so 10 m, at time t 0 seconds a) Derive expressions for acceleration, a(t), and position, s(t), using the integral/derivative relationships for acceleration, velocity, and position as functions of time. b) Using your formulas from part a, calculate the velocity, acceleration, and position of the particle for every 1...
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...
A particle moves according to a law of motion s = ft), t 0, where t is measured in seconds and s in feet. t)-te-t2 (a) Find the velocity at time t (in ft/s) v(t) e (b) What is the velocity after 2 s? (Round your answer to two decimal places.) v(2) ft/s (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total...
5. The following graph represents the velocity of an object, moving along a horizontal line as a function of time. Express all answers to two significant figures. East is the positive direction and West is negative. (6 marks) Velocity Vs. Time 10 Velocity. (m/s) 10 12 14 -6 Time, t(s) a) Determine the acceleration of the object at 1.0s. b) Determine the average velocity of the object between 4.0 and 8.0 s. c) Over what time interval(s), if any, is...
The velocity of a particle traveling in a straight line is given by v (6t-3t2) m/s, where t is in seconds. Suppose that s 0 when t0. a. Determine the particle's deceleration when t3.6s b. Determine the particle's position when t 3.6 s C. How far has the particle traveled during the 3.6-s time interval? d. What is the average speed of the particle for the time period given in previous part?