4. A ball with a mass of 5 kg experiences an acceleration of 10 m/s. What is the nel force acting on the ball?

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 ?

20. threshold braking in the vehicle's braking system occurs when a. the brake pedal is pushed, heel on floorboard, with full foot pressure. b. the brakes are exerting full braking power, without traction loss. c. the driver begins pushing down the brake pedal, with moderate slowdown. d. the brakes just begin to take hold with a gradual slowdown.

The system is released from rest with the cable taut, and the homogeneous cylinder does not slip on the rough incline. determine the angular acceleration of the cylinder and the minimum coeffi cient s of friction for which the cylinder will not slip.