The vector position of a particle varies in time according to the expressionỉ = 3.00i – 6.00fj, where i is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the accelera- tion of the particle as a function of time. (c) Calculate the particle's position and velocity at t= 1.00 s.

The vector position of a particle varies in time according to the expressionỉ = 3.00i – 6.00fj, where i is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the accelera- tion of the particle as a function of time. (c) Calculate the particle's position and velocity at t= 1.00 s.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 3P: A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial...

See similar textbooks

Similar questions

A football is thrown horizontally with an initial velocity of116.6 m>s2xn . Ignoring air resistance, the average acceleration ofthe football over any period of time is 1-9.81 m>s22yn . (a) Find thevelocity vector of the ball 1.75 s after it is thrown. (b) Find the magnitude and direction of the velocity at this time.
The vector position of a particle varies in time according to the expression r (3.00i 6.00t 2 j) m. (a) Findexpressions for the velocity and acceleration as functions of time. (b) Determine the particle’s position andvelocity at t 1.00 s
Does the acceleration vector always point in the direction in which an object is moving? If so,explain why. If not, describe a situation in which the direction of the acceleration is not thesame as the direction of motion
The vector position of the particle varies in time according tot the expression r= (3.00i - 6.00t^2j)m. (a) Find expressions for the velocity and acceleration of the particle as function of time. (b) Determine the particle's position and velocity at t= 1.00s
Let the position vector (with its tail at the origin) of a moving particle be~r(t) = t^(2)ˆi − 2tˆj + (t^(2) + 2t)ˆk, where ~r(t) is measured in meters and t is measured in seconds.(a) Find the acceleration vector and the magnitude of the particle at time t.(b) Find the acceleration vector and the magnitude of the particle when it passes throughthe point (4, -4, 8).
The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).
An object moves in the x-y plane with coordinates given as a function of time by: x(t) = Rcos(ωt) y(t) = Rsin(ωt) where R and ω are constants. What is the velocity vector of the object at any time t?
The vector position of a particle varies in time according to theexpression r = 3.00i - 6.00t2 j ⁄ , where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as afunction of time. (b) Determine the acceleration of the particle as afunction of time. (c) Calculate the particle’s position and velocity at t =1.00 s.
In the blizzard of ’88, a rancher was forced to drop hay bales from an airplane to feed her cattle. The plane flew horizontally at 160 km/hr and dropped the bales from a height of 80 m above the flat range, (a) She wanted the bales of hay to land 30 m behind the cattle so as to not hit them. Where should she push the bales out of the airplane? (b) To not hit the cattle, what is the largest time error she could make while pushing the bales out of the airplane? Ignore air resistance.
A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.
If the initial velocity vector of a particle is vo 8i - 2j m/s, and after time t 5 s its v 2i+ 6j m/s,then find the acceleration vector a (in m/).
A projectile is launched with a launch angle of 30° with respect to the horizontal direction and with an initial speed of 26 m/s. How do the vertical and horizontal components of the projectile's velocity vary with time?The initial velocity in the x-direction vx0 is related to the initial speed by vx0 = v0 cos 30°. The constant velocity in the x-direction means that the equation describing the time dependence of x for the particle, with x0 taken as 0, is x = x0 + vx0t = 0 + m/s t. The equation for the vertical coordinate, which is constantly accelerating downward at g = 9.8 m/s2, is y = y0 + vy0t − 1 2 gt2 = m/s t + m/s2 t2.