A particle moves in a straight line with velocity v ms^-1. Its initial velocity is u ms^-1. At any time t, the velocity v is given by the equation (dv/dt) + 3 + v^2=2. Prove that the particle comes instantaneously to rest after tan^-1 seconds. Given that the particle moves s metres in t seconds, show that the particle first comes to rest after a displacement of 1/2 ln (1+u^2) metres.

Imagine an isolated positive point charge q (many times larger than the charge on a single proton). there is a charged particle a (whose charge is much smaller than charge q) at a distance from the point charge q. on which of the following quantities does the magnitude of the electric field created by charge q at particle a's position depend? check all that apply.the type of the charge on the charged particle athe relative orientation between q and a (while the distance between q and a is fixed)the specific location of the charged particle a (while the distance between q and a is fixed)the amount of the charge on the point charge qthe specific location of the point charge q (while the distance between q and a is fixed)the distance between the point charge q and the charged particle athe amount of the charge on the charged particle a