A particle has a position vector given by r(t)= 30t i + (40t - 5t^2)j, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of time.

A particle has a position vector given by r(t)= 30t i + (40t - 5t^2)j, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of time.

Name: A particle has a position vector given by r(t)= 30t i + (40t - 5t^2)j,
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: A particle has a position vector given by r(t)= 30t i + (40t - 5t^2)j, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of time.

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 6P: At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of...

See similar textbooks

Similar questions

At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.
A particle has a position vector given by r(t)=30 t i + (40t-tt^2) i, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of time.
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?
A particle has a position vectors given r(t) = 30t i + (40t -5 t²) j, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of 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
From the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim/s and moves in the xy plane with a constant acceleration of a=(-9.0hati+3.0hatj)m/s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?
Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = eti + sin2tj + cos3k, v(0) = i r(0) = j
The position r→ of a particle moving in an xy plane is given by r→=(3.00t^3−7.00t)i^+(6.00−2.00t^4)j^ with r→ 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).
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/).
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).
A skater is gliding along the ice at 2.2 m/s, when she undergoes an acceleration of magnitude 1.2 m/s2 for 3.0 s. At the end of that time she is moving at 5.8 m/s. (a) What must be the angle between the acceleration vector and the initial velocity vector?
An ice skater is gliding along at 2.1 m/s , when she undergoes an acceleration of magnitude 1.4 m/s2 for 3.0 s. After that she's moving at 6.3 m/s . Find the angle between her acceleration vector and her initial velocity vector.