The vector position of a particle varies in time according to the expression r = 3.00i - 6.00t^2 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. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particles position and velocity at t = 1.00s.

The vector position of a particle varies in time according to the expression r = 3.00i - 6.00t^2 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. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particles position and velocity at t = 1.00s.

Name: The vector position of a particle varies in time according to the expr
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: The vector position of a particle varies in time according to the expression r = 3.00i - 6.00t^2 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. (b) Determine the acceleratio

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

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 11P: A particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in...

See similar textbooks

Similar questions

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
On a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x direction of ax = 3.41 m/s^2, while the other produces an acceleration in the y direction of ay = 7.34 m/s^2. At the end of the firing period, the craft has velocity components of vx = 1860 m/s and vy = 4290 m/s. Find the (a) magnitude and (b) direction of the initial velocity. Express the direction as an angle with respect to the +x axis.
A football is placed at rest on the field with initial coordinates x0 = 0 and y0 = 0. The ball is then kicked and thereby given an initial velocity of magnitude v0 = 23.6 m/s and direction θ0 = 36.3o above the horizontal. Ignore the effects of air resistance. Initial horizontal component of the velocity v0x = Initial vertical component of the velocity v0y = Horizontal component of the acceleration ax = Vertical component of the acceleration ay = Enter the equation for the horizontal position versus time, x(t) = Enter the equation for the vertical position versus time, y(t) = Enter the equation for the horizontal velocity versus time, vx(t) = Enter the equation for the vertical velocity versus time, vy(t) = Enter the equation for the total velocity versus time, v(t) = Enter the equation for the angle of the velocity vector versus time, θ(t)= Enter the maximum height of the football Enter the range of the football Enter the time it takes for the football to reach its maximum…
A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. ( m/s) + ( m/s) At the maximum height, the speed of the cannon ball is v = m/s and the magnitude of its acceleration is a = m/s2. The time needed to reach maximum height is t = s. The maximum height reached by the cannon ball is H = m.
In the two-dimensional motion, what is the magnitude of the y component of the velocity of the projectile when it is at its apex of trajectory? Select one: a. Velocity is equal to the initial velocity b. Velocity is 9.81 m/s c. Velocity is equal to the x component d. Undetermined e. Velocity is 0 m/s
Suppose the baseball is struck from the edge of a cliff such that y0 = 30 m and x0 = 0. The components of the initial velocity are v0x = 20 m/s and v0y = 0. What is the x coordinate of the baseball when it lands on the ground at y = 0? (Write only the numerical value rounded to a whole number and exclude the unit)
The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?
If the vector components of the position of a particle moving in the xy plane as a function of time are x = (2.8 m/s2)t2 and y = (6.4 m/s3)t3, at what time t is the angle between the particle's velocity and the x axis equal to 45°?
The velocity of a particle moving in the x-y plane is given by (6.98i + 6.68j) m/s at time t = 7.60 s. Its average acceleration during the next 0.014 s is (4.1i + 5.4j) m/s2. Determine the velocity v of the particle at t = 7.614 s and the angle θ between the average-acceleration vector and the velocity vector at t = 7.614 s.Answers:v = ( _____ i + _____ j) m/sθ = _____ °
A particle moves in the xy plane, starting from the origin at t = 0 with an initial velocity having an x-component of 10 m/s and ay-component of -5 m/s. The particle experiences an acceleration only in the x-direction, given by ax = 3 m/s2 please find 1. the total velocity vector at t=2 s.2. the speed of the particle at t=2 s.
A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y2 = [120(10^3)x] m. If the x component of acceleration is ax = (1/4t^2)m/s^2, where t is in seconds, determine the magnitude of the rocket’s velocity and acceleration when t = 10 s.
A car moves along a horizonatal road with constant velocityv0 = v0, x^ii = (30.06 m/s)^i until it encounters a smooth inclined hill. It climbs the hill with constant velocity. v1=v1x^+v1y^j = (44.2 m/s)^i + (3.23 m/s)^jWhat is the expression in cartesian unit vector notation, for average acceleration of the car during the given time period using the symbols provided?