4. A long time ago, in a galaxy far far away, a Death Star was constructed....

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4. A long time ago, in a galaxy far far away, a Death Star was constructed. Its surrounding force field caused a particle at distance r relative to the Death Star to experience an acceleration r = xr where is a constant. Show that particles move in this field with constant speed. Show, moreover, that the magnitude of acceleration is also constant. (a) A particle is projected radially with speed v from a point r = Rr on the surface of the Death Star. Show that its trajectory is given by r = (vt + R) (b) By considering the second derivative of rr show that, for any particle moving in the force field, the distance r to the centre of the Death Star is given by r = v (t to) + r where to and ro are constants and v is the speed of the particle. Obtain an expression for r r and show that |r| = Avro. 4. A long time ago, in a galaxy far far away, a Death Star was constructed. Its surrounding force field caused a particle at distance r relative to the Death Star to experience an acceleration r = xr where is a constant. Show that particles move in this field with constant speed. Show, moreover, that the magnitude of acceleration is also constant. (a) A particle is projected radially with speed v from a point r = Rr on the surface of the Death Star. Show that its trajectory is given by r = (vt + R) (b) By considering the second derivative of rr show that, for any particle moving in the force field, the distance r to the centre of the Death Star is given by r = v (t to) + r where to and ro are constants and v is the speed of the particle. Obtain an expression for r r and show that |r| = Avro.