Question

A 3.00-kg particle starts from the origin at time zero. Its velocity as a function of...

A 3.00-kg particle starts from the origin at time zero. Its velocity as a function of time is given by v = (3t^2) i+ (2t) j where v is in meters per second and t is in seconds.

(a) Find its position at t = 1s.

(b) What is its acceleration at t = 1s ?

(c) What is the net force exerted on the particle at t = 1s ?  

(d) What is the net torque about the origin exerted on the particle at t = 1s ?  

(e) What is the angular momentum of the particle at t = 1s ?  

(f) What is the kinetic energy of the particle at t = 1s ?

(g) What is the power injected into the system of the particle at t = 1s ?

please answer them all together since they are related to each other

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A 14.00 kg particle starts from the origin at time zero. Its velocity as a function...
A 14.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by v with arrow = 9t2î + 4tĵ where v with arrow is in meters per second and t is in seconds. (Use the following as necessary: t.) (a) Find its position as a function of time. r =________ (c) Find its acceleration as a function of time. a=_______m/s^2 ( (d) Find the net force exerted on the particle as...
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) A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and...
A) A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and moves in the xy plane with a varying acceleration given by ?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and t is in seconds. i) Determine the velocity of the particle as a function of time. ii) Determine the position of the particle as a function of time. (Explanation please )
A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and moves...
A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and moves in the xy plane with a varying acceleration given by ?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and t is in seconds. i) Determine the VELOCITY and the POSITION of the particle as a function of time.
A particle starts at the origin with initial velocity ⃗v(0) = ⃗i − ⃗j + ⃗k....
A particle starts at the origin with initial velocity ⃗v(0) = ⃗i − ⃗j + ⃗k. Its acceleration is ⃗a(t) = 4t⃗i + 3t⃗j − ⃗k. Find its position at t = 3.
The position vector of a particle of mass 2kg is given as a function of time...
The position vector of a particle of mass 2kg is given as a function of time by: r = (4i + 2t j + 0k) m, when t is given in seconds. (a) Determine the angular momentum of the particle as a function of time. (b) If the object was a sphere of radius 5 cm, what would be its rotational frequency?
At time t,  r→ = 8.60t2 î - (4.90t + 6.10t2) ĵ gives the position of a...
At time t,  r→ = 8.60t2 î - (4.90t + 6.10t2) ĵ gives the position of a 3.0 kg particle relative to the origin of an xy coordinate system ( r→ is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 4.50 s (b) Is the magnitude of the particle’s angular momentum relative to the origin increasing, decreasing, or unchanging?
At time t,  r→ = 1.70t2 î - (7.60t + 7.80t2) ĵ gives the position of a...
At time t,  r→ = 1.70t2 î - (7.60t + 7.80t2) ĵ gives the position of a 3.0 kg particle relative to the origin of an xycoordinate system ( r→ is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 6.50 s (b) Is the magnitude of the particle’s angular momentum relative to the origin increasing, decreasing, or unchanging?
A particle is to move in an xy plane, clockwise around the origin as seen from...
A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle at time t = 7.6 s if the magnitude of its angular momentum about the origin is (a)8.4 kg·m2/s, (b)8.4t2 kg·m2/s3, (c)8.4t1/2 kg·m2/s3/2, and (d)8.4/t2 kg·m2*s?
A moving particle starts at an initial position r(0) = <1, 0, 0> with initial velocity...
A moving particle starts at an initial position r(0) = <1, 0, 0> with initial velocity v(0) = i - j + k. Its acceleration is a(t) = 4t i + 4t j + k. Find its velocity, v(t), and position, r(t), at time t.