A particle particle. moves with position function r(t) = 4/2ti – e4tj+e*k. Find the acceleration of the

Q: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

A:

Q: A particle moves along the x-axis with acceleration at any given time t as a(t) = 3t+4t+6,jf the…

A:

Q: If a(t) is the acceleration of a moving particle at time t , then Ja(t) dt is the velocity at time t…

A:

Q: 4. The function a(t) = 3t² – 20t + 27 describe the acceleration of a particle moving along a line.…

A: Given that: Acceleration function, a(t)=3t2-20t+27

Q: 1. Given r(t) = 2 cos t i + 2 sintj+ 10tk; 0 <t< 2n , find the tangential and normal components of…

A:

Q: give the acceleration a = d2s/dt2, initial velocity,and initial position of an object moving on a…

A: We know that velocity, y=dsdt and acceleration, a=dydt. We have given a=-4sin 2t. To find velocity y…

Q: a) When is the particle at rest? b) During what time interval is the particle moving right? Left?…

A: (a) The particle is at rest when velocity is zero. And we know velocity V(t) is the derivative of…

Q: アー テー Solve using the Laplace transform y' – y = e3t , y(0) = 2

A:

Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

A:

Q: - particle's position for t > 0 is given by s (t) = 2t³ + 2t² – 5t +2. What s the acceleration at t…

A: Given query is to find the acceleration ate t= 1.

Q: 5) The position vector of a particle is given by s(t) = 3t2 – 3t + 4.Find the time at which the…

A:

Q: Given the acceleration a=d^2s/dt^ 2​, initial​ velocity, and initial position of a body moving on a…

A: Given :- a=-81sin9t, v(0)=9,  s(0)=-7 Here, a is accelerationdvdt, v is velocity dsdt and s is…

Q: A particle moves along a coordinate line in such a way that its velocity at any time t is given by…

A: We have, a particle moves along a co-ordinate line in such a way that its velocity at any time t is…

Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

A:

Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

A: By using the general formula of Newton's law of motion, we can calculate the position of particle at…

Q: 3. Use the given acceleration function to find the velocity and position functions, and then find…

A: The given vectors are: a(t)→=i^+2j^+k^v(0)→=2j^r(0)→=i^   The relations between position, velocity…

Q: 5) The position vector of a particle is given by s(t) = 2t² – 3t + 1.Find the time at which the…

A: answer = 2.5 sec   explanation is given in below step

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Given that       The position of the particle at time t is given by  s(t) = t2 -8t + 15. Here we…

Q: 5) The position vector of a particle is given by s(t) = 2t² – 5t + 4.Find the time at which the…

A:

Q: A particle is moving with acceleration a(t) = 6t + 16. its position at time t = velocity at time t =…

A:

Q: The position of a particle moving along a straight line is given by s(t) : 1 du. The acceleration at…

A:

Q: 5) The position vector of a particle is given by s(t) = 2t2 – 2t + 2.Find the time at which the…

A: s(t) = 2t2-2t+2∴ s(1) = 2(1)2-2(1)+2 = 2and∴ s(6) = 2(6)2-2(6)+2 = 72-12+2 =62∴ average velocity =…

Q: A particle is moving with acceleration a(t) = 18t + 4. its position at time t = 0 is s(0) = 5 and…

A:

Q: Given a particle is moving in a curve r(t) = cos 8t i + sin 8tj+ 8t k. Find the normal component of…

A: You need to find the velocity and acceleration from the given r(t) and then use the formula to get…

Q: 3. Find the position and velocity of the particle if its acceleration is a(t)=-cos(t)i – sin(t)j…

A:

Q: Q.3 a) If acceleration components of an electron are given by d²x - b d²y 0, dt dy dx b- = a dt dt?…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find the instantaneous velocity of the particle described in the figure below at the following…

A: Topic :- Differentiation

Q: 2. A particle moves with position s = t* – 4t3 – 201² + 20t when t >0. At what time does the…

A:

Q: RT a P = V -b T²v(v+b) – b 1/2

A:

Q: Find the position of a body moving on a coordinate line at time t for an acceleration a= dt² initial…

A:

Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

A:

Q: The position of the particle at time t is given by s(t) = t2 - 6t + 8. %3D The particle is moving…

A: To find the value of t particle moves from left to right

Q: An object with an initial velocity of v(1) = 2 has an acceleration of a(t ) = %3D ( 2t – 1) What is…

A:

Q: 3. If s(t) = 3f³ -1812+5, 0<1<3 gives the position of a moving particle, find the velocity and…

A: Here given position function s(t)= 3t3-18t2+5

Q: 3 find the invers laplace f(t) = S+3 s²+3

A:

Q: 5) The position vector of a particle is given by s(t) = 2t2 – 2t + 2.Find the time at - which the…

A:

Q: 5) The position vector of a particle is given by s(t) = 2t2 – 5t + 4.Find the time at which the…

A: Given,  The position vector of a particle a given by  st = 2t2-5t+4  We have to find the time at…

Q: Evaluate the position function r (t) if we have the velocity function and initial condi- tions. 1 6t…

A: Given

Q: A particle is moving with acceleration a(t)=30t +18. Its position at time t=0 s(0)=11 and its…

A: Explanation of the answer is as follows

Q: Find the position of the particle at time t=4. Is the particle moving toward the origin or away from…

A: If the velocity function is given then by integration we will calculate the position of the particle…

Q: A particle's position at time t is s(t) = 2t2 - 4t + 1. Compute the AVERAGE velocity over the…

A:

Q: A particle moves in a straight line from the origin (at t = Q) with given initial velocity vo and…

A:

Q: 5) The position vector of a particle is given by s(t) = 2t² – 4t + 4.Find the time at which the…

A: Find time t. Given: Position vector, s(t)=2t^2-4t+4.

Q: Q2. Let a(t) = 2j + 6tk be the acceleration of a particle at time t. If r(0) = −2i+j and v(0) = i,…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving a a(t)…

A:

Q: 11. Find the position r(t) of an object if the acceleration is a(t) = and the initial position is…

A: We have to find out r vector

Q: 5) The position vector of a particle is given by s(t) = 2t2 – 2t + 4.Find the time at which the…

A:

Q: 4x Find the gradient field F = Vo for the potential function p == y F =

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.