IB Physics Relativity

Here is part of a question on Special Relativity taken from Columbia University's Physics Qualifying Examination in 2016. It was set by renown physicist and author Brian Greene. HL students aiming for a 7 must do extra reading to broaden their knowledge of Physics. Professor Greene's books make a good start. An asteroid is on a collision course with a space station located 5000 light minutes from the Earth. The asteroid is moving away from the Earth toward the space station at a speed 3/5c along a trajectory which is a straight line connecting the Earth and the space station. To save the station, NASA launches a missile from Earth at 4/5c. When the missile is launched, NASA determines that the asteroid is 400 light-minutes from Earth. How many minutes should NASA set on a timer located on the missile so that it will explode just as it catches the asteroid? [1200 minutes]

HSC Physics Assessment Task

A common Assessment Task in HSC Physics is to release a ball bearing from rest on a track inclined at a small angle to the horizontal and measure the time taken (t) to move various distances (d). The average speed is then calculated (v=d/t) and a graph of v-t is drawn. A common mistake is to then say that the gradient of this graph is the acceleration of the ball. Why is this incorrect? How do we determine the acceleration of the ball?