An object's position is given by r(t) = (150-t2 + 1/12t3)i + (200+5t-2.5t2, + 1/18t3)j where...
The vector position of an object varies according to r(t) = (24.0 m)i + [(2.00 m/s2)t2]j, where t is in seconds. (a) Determine the magnitude of the position vector at t = 5.00 s. (b) Determine the magnitude of the velocity vector at 5.00 s. A boy stands on a diving board and throws a stone into a swimming pool. The stone is thrown from a height of 2.93 m above the water surface with a velocity of 5.26 m/s...
Suppose the position vector for a particle is given as a function of time by r(t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct + d, where a - 1.70 m/s, b = 1.50 m, c = 0.116 m/s, and d = 1.04 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 4.05 s. m/s (b) Determine the velocity at t = 2.05 s. m/s...
The vector position of a particle varies in time according to the expression r-7.40 i-8.20t2 j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s2 (c) Calculate the particle's position and velocity...
The position of a particle is given by r = (at2)i + (bt3)j + (ct-2)k, where a, b, and c are constants. a) What is the velocity as a function of time? b) What is the acceleration as a function of time? c) Suppose a = 4.48 m/s2, b = -2.63 m/s3, and c = -82.7 ms2. What is the particle’s speed, in m/s, at t = 2.46 s? d) Referring to the values given in part (c), what is...
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
t the Wackes in ersed from e with mantude of 15 The Black I haa t he block 2 has mass and Neck has a mass Calculate c t of inte friction between black and a (A) 0.34 B) 0.45 (C) 0.87 (D) 0:54 0.99 14 The work of a given force has its maximum positive value when CA) The vector of displacement and force are at the same direction B) The vector of displacement and force are at the...
A car, traveling due north, has an initial velocity of 18 m/s accelerates for 9 s for a distance of 180 m. What is the velocity of the car after the acceleration? (5) A remote controlled car is moving through a parking lot described by the position function r(t) = [2.5 m - (0.015 m/s^2) t^2] i - [0.6 m - (0.1 m/s) t + (0.032 m/s2) t^2] j. What is the speed of the toy car at t =...
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
QUESTION 8 The velocity of a particle is v-1 9 i + (3-2) j m/s, where t is in seconds. If r:0 when particle in the y direction during the interval t 1 sto t 4 s 0, determine the displacement of the QUESTION 8 The velocity of a particle is v-1 9 i + (3-2) j m/s, where t is in seconds. If r:0 when particle in the y direction during the interval t 1 sto t 4 s...