A 13.00 kg particle starts from the origin at time zero. Its velocity as a funct

Question

A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by v with arrow = 8t2i + 3tj 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 with arrow = (b) Describe its motion qualitatively. (c) Find its acceleration as a function of time. a with arrow = m/s2 (d) Find the net force exerted on the particle as a function of time. F with arrow = N (e) Find the net torque about the origin exerted on the particle as a function of time. = N · m (f) Find the angular momentum of the particle as a function of time. L with arrow = kg · m2/s (g) Find the kinetic energy of the particle as a function of time. K = J (h) Find the power injected into the particle as a function of time. P = W

Explanation / Answer

v = 8t^2 i + 3t j

a) Position = r = intgration(v*dt) = (8/3)t^3 i + (3/2)t^2 j

b) The particle is moving in x-y plane depending on time.

c) Acc. = a = dv/dt = 16t i + 3 j

d) Force = F = ma = 208t i + 39 j

e) Torque = = r x F = [(8/3)t^3 i + (3/2)t^2 j] x [ 208t i + 39 j] = (104 - 312) t^3 k^= -208 t^3 k^

f) the angular momentum = L = (-208/4)t^4 k^ = -52t^4 k^

g) KE = 0.5*m*v^2 = 416t^4 i + 58.5t^2 j

h) Power = KE/t = 416t^3 i + 58.5t j

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