Apiece of interstellar debris (with mass m and moving at speed v relative to a deep-space observer) explodes into two pieces, one of them 3 times as massive as the other. the less massive piece stops as seen by the observer (in the observer's frame of reference).

how does the kinetic energy of the system change as a result of the explosion, as seen in the observer's frame of reference? express your answer as a ratio of the change in kinetic energy to the initial kinetic energy.

your answer should be unitless since it is a ratio.

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

Under the action of a constant force an object accelerates at 7.8 m/s2. what will the acceleration be if (a) the force is halved? (b) the object's mass is halved? (c) the force and the object's mass are both halved? (d) the force is halved and the object's mass is doubled?

The energy equivalent of the rest mass of an electron is