6. The instructions for your toy car set say that the max centripetal acceleration the cars can withstand without falling out of the track is 3.8 m/s. You notice that the toy cars fly
off the track when they move faster than 1.1 m/s, so what is the radius in meters of the
curve in your track?

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Assuming weightless pulleys and 100% efficiency, what is the minimum input force required to lift a 120 n weight using a single fixed pulley?

What type of light does this light bulb produce most (i.e. at what wavelength does the spectrum have maximum intensity)?