A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j...

A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j where x(t) = 10t² and y(t) = -3t + 2, with x and y in meters and t in seconds.

(a) Find the momentum of the particle at time t = 1.00 s.
(b) Find the angular momentum about the origin at time t = 3.00 s.

Expert Solution

genius_generous answered 2 years ago

A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j...

A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters and t in seconds. (a) Find the momentum of the particle at time t = 1.00 s. (b) Find the angular momentum about the origin at time t = 3.00 s.

A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2...

A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters and t in seconds. (a) Find the average velocity for the time interval from 1.00 s to 3.00 s. (b) Find the instantaneous velocity at t = 1.00 s. (c) Find the average acceleration from 1.00 s to 3.00 s. (d) Find the instantaneous acceleration at t = 1.00 s.

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t...

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t + 3.50t2 − 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.55 s? F with arrow = ______ N

Find the distance traveled by a particle with position (x, y) as t varies in the...

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin2 t, y = 5 cos2 t, 0 ≤ t ≤ 5π What is the length of the curve?

A particle of mass 2.00 kg is attached to a spring with a force constant of...

A particle of mass 2.00 kg is attached to a spring with a force constant of 300 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 4.00 m. A 7.00 kg object is dropped vertically on top of the 2.00 kg object as it passes through its equilibrium point. The two objects stick together. (a) Does the amplitude of the vibrating system increase or decrease as a result of the collision? decreases increases no change (b)By...

The position of a particle is r={(3t3−2t)i−(4t1/2+t)j+(3t2−2)k}m, where t is in seconds. Part A Determine the...

The position of a particle is r={(3t3−2t)i−(4t1/2+t)j+(3t2−2)k}m, where t is in seconds. Part A Determine the magnitude of the particle's velocity when t = 0.5 s . Express your answer with the appropriate units. v=? Part B Determine the magnitude of the particle's acceleration when t = 0.5 s . Express your answer with the appropriate units. a=?

A particle with mass m moves on the surface of a cylinder with radius R. At...

A particle with mass m moves on the surface of a cylinder with radius R. At the same time, the force F = -kr on the particle affects it through the z axis. Using the z-and θ generalized coordinates, find the system's hamitonians. Solve the Hamilton equation after defining the conservative quantities.

Suppose r(t)=cos(πt)i+sin(πt)j+2tk represents the position of a particle on a helix, where z is the height...

Suppose r(t)=cos(πt)i+sin(πt)j+2tk represents the position of a particle on a helix, where z is the height of the particle. (a) What is t when the particle has height 8? (b) What is the velocity of the particle when its height is 8? (c) When the particle has height 8, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms...

A particle (mass = 6.7 x 10-27 kg, charge = 3.2 x 10-19 C) moves along...

A particle (mass = 6.7 x 10-27 kg, charge = 3.2 x 10-19 C) moves along the positive x axis with a speed of 4.1 x 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 5.0 m into the field. What is the magnitude of the electric field (in N/C) ?

a particle moves aling a straight line and its position at time t is given by...

a particle moves aling a straight line and its position at time t is given by s(t)= (t^3)-13.5t^2+54t where s is measured in feet and t is seconds. consider t in the interval [0,infinity) 1) when is the particle moving in the positive direction? ( i tried (0,3) U(6, infinity) but it didnt work) 2) what is the total distance the particle travels travels between time 0 and time 7 3) when is the particle speeding up? 4) when is...

Question

A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j...

Solutions

Expert Solution

Related Solutions

A particle of mass 2.00 kg moves with position r(t) = x(t) i + y(t) j...

A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2...

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t...

Find the distance traveled by a particle with position (x, y) as t varies in the...

A particle of mass 2.00 kg is attached to a spring with a force constant of...

The position of a particle is r={(3t3−2t)i−(4t1/2+t)j+(3t2−2)k}m, where t is in seconds. Part A Determine the...

A particle with mass m moves on the surface of a cylinder with radius R. At...

Suppose r(t)=cos(πt)i+sin(πt)j+2tk represents the position of a particle on a helix, where z is the height...

A particle (mass = 6.7 x 10-27 kg, charge = 3.2 x 10-19 C) moves along...

a particle moves aling a straight line and its position at time t is given by...