object at timet is given by the function f(t) = 4t3 -18t 2 + 24t, where...
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...
An object is moving around the plane with velocity given by y(t) = (3,2t) for timet > 0. a) If the object crosses the origin (0,0) at timet = 2 give the vector valued function representing the object's position in the form ř(t) = ((t), y(t)). b) Give the vector valued function a(t) that represents the object's acceleration.
(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...
An object thrown vertically upward from the surface of a celestial body at a velocity of 24 m/s reaches a height of s = -0.6t2 + 24t meters in t seconds. a. Determine the velocity v of the object after t seconds. b. When does the object reach its highest point? c. What is the height of the object at the highest point? d. When does the object strike the ground? e. With what velocity does the object strike the ground? f. On what intervals is...
What is the Fourier transform of: Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = 16 / (t)-sin(18t)? Question 2 (1 mark) Attempt 1 What is the Fourier transform of: f(t)-5-isin(18t)? 3Tt Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = skipped 16 / (t)-sin(18t)? Question 2 (1 mark) Attempt 1 What is the Fourier transform of: f(t)-5-isin(18t)? 3Tt Your...
The height h (in feet) of an object falling from a tall building is given by the function h(t) 400 16, where t is the time elapsed in seconds (a) After how many seconds does the object strike the ground? (b) What is the average velocity of the object from t- o until it hits the ground? (c) Find the instantaneous velocity of the object after I second ft/sec Find the instantaneous velocity of the object after 2 seconds. ft/sec...
A particle moving along the x axis has a position given by x=(24t-2t^3)m where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?
Suppose f is a quadratic function that has roots at I = - 4 and I = 8, and f(0) = 16. We will write a function formula for f. a. Sketch a graph of f based on the information you are given. b. We can write f as f(x) = c(x - 1)(x - ) where x < , and c is some constant number What are the values of 3, and az? O2 = -2/4(x+4)(x-8) Preview Preview c....
An object moves along a line where s(t) = t^3 − 12t^2 + 36t − 30 (where s(t) is in feet and t in seconds). 1) When is the velocity 0? 2) When is the velocity positive? 3) When is the object moving to the left? 4) When is the acceleration positive? 5) Sketch a picture of its motion. Please label the numbers of the answers.
Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, 8 (t). Question 1 How much does the position change over the time interval (0,4) Answer with a number only (units are feet) 36 Question 2 Question: Think back to the total change theorem. What additional Information would allow us to find a(4), the object's position at time t =...