A particle moves according to the function θ = t3-5t2 + 4 where θ is in...
3. A particle moves according to the function 3-5t2 4 where 0 is in radians and t is in seconds. (a) Find the angular velocity of the particle at 1 s and t-2 s, (b) Find the average instantaneous acceleration between t-1 and t = 2 s. (c) what is the angular position of the particle at the first time when the angular velocity is 0?
Need both answered please!
1. A particle moves with acceleration function a(t) = 8t + 5. Its initial velocity is v(O) = -4 cm/s and its initial displacement is s(0) = 5. Find its position after t seconds. s 2. The equation of motion of a particle is S = t3 - 9t, where s in meters, and t is in seconds. Find a) The velocity and acceleration as a function oft b) The acceleration after 4 seconds.
The angular position of a point on the rim of a rotating wheel is given by θ = 6.0t - 2.0t2 + t3, where θ is in radians and t is given in seconds. (a) What is the angular velocity at t = 2 s? rad/s (b)What is the angular velocity at t = 4.0 s? rad/s (c) What is the average angular acceleration for the time interval that begins at t = 2 s and ends at t =...
A particle moves along the x axis according to the equation x = 1.91 2.99t-1.00e, where x is in meters and t is in seconds. (a) Find the position of the particle at t 2.90 s (b) Find its velocity at t- 2.90 s m/s (c) Find its acceleration at t 2.90s m/s? My Note (a) Can the velocity of an object at an instant of time be greater in magnitude than the average velocity over a time interval containing...
A particle moves falling vertically through a viscous liquid. The velocity is recorded as a function of time and it is observed that it corresponds approximately to the following function: v (t) = 10 (1 - exp (-t)), t in seconds v in m / s. a) Graph velocity versus time. Describe what happens in words. b) Calculate the instantaneous acceleration of the particle and subtract from it the acceleration of gravity (10 m / s²). Graph the resulting acceleration,...
Use Python to solve each problem. 2. A particle moves according to a law of motion s = t 3 − 12t 2 + 24t, t ≥ 0. a) Find the velocity at time t. b) What is the velocity after 1 second? c) When is the particle at rest? d) Sketch the position function on t ∈ [0, 6] to determine when the particle is moving in the positive direction on that interval. e) Find the total distance traveled...
Given position x = 2t + 5t2 (where x is in meters and t is in seconds): A. Calculate the average velocity over the time interval t = 1 s to t = 4 s. Units: m.s-1 B. What is the instantaneous velocity at t = 4 s? Units: m.s-1 C. What is the acceleration of the object? Units: m.s-2 D. In which direction is the object accelerating?
Average and Instantaneous Velocity A particle moves along the x axis. Its position varies with time acording to the expression x =-4t + 2t2, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times...
A particle moves along a straight a) The average velocity on the line with equation of motion interval [3,4] s= f(t) = t? - 60 + 10, b) The instantaneous velocity. Where S is measured in meters and t in seconds. find the C) The instantaneous velocity when following: t = 4 seconds. The growth of a bacterial population is represented by the function f(t) = 1 + 5t - 2t2 Where t is the time measured in hours find...
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...