Question

article starts from the origin at ti 20. Q C A 5.00-kg p Its velocity as a function of time is given by where v is in meters per second and t is in seconds its position as a function of time. (b) Desc qualitatively. Find (c) its acceleration as a function of time (d) the net force exerted on the particle as a function of time, (e) the net torque about the origin exerted on the particle as a function of time, (f) the angular momentum of the particle as a function of time, (g) the kinetic energy (a) Find ribe its motion

Answer 1

Given v vector = 6 t^2 i^+ 2 t j^v vector = d x vector/dt = 6 t^2 i^+ 2 t j^integral dx = integral 6 t^2 i^+ 2 t j^dt x = 2 t^3 i^+ t^2 j^a vector = dv vector/dt = 12 t i^+ 2 j^at t = 1 a = 12 i^at t = 2 a = 24 i^at t = 3 a = 36 i^motion is accelerated motion. A vector = du vector/dt = 12 t i^+ 2 j^net force f = m a = 5.0 (12 t i^+ 2 j^) = 60 t i^+ 10 j^tou vector = r vector Times f vector Vertical-bar i^2 t^3 60 t j^t^2 10 k^0 0 Vertical-bar = -40 t^3 k^l = v r implies 5[6 t^2 i^+ 2 t j^] [2 t^3 i^+ t^2 j^] implies 5 Times [12 t^5 + 2 t^3] = 60 t^5 + 10 t^3