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.

Lin yao looks at the back of a spoon. how should she describe her reflection? upside down and smaller upside down and larger right-side up and smaller right-side up and larger

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.

(a) if the pressure in gas is doubled while its volume is held constant, by what factor do (i) vrms and (ii) change? (b) is it possible to boil water at room temperature (20oc) without heating it? explain.