In the experiment shown above, an astronaut of mass m propels himself with a rocket which applies constant force F .
The astronaut begins at rest at position 0 m. He turns on the rocket, which applies the force over a distance d , when the rocket is shut off. The astronaut then coasts at constant speed.
While he is moving at constant speed, he travels between two photogates, shown in red in the diagram. The distance between the photogates is x ; the time for the astronaut to traverse the photogates is t . The experiment is repeated multiple times. In each trial, the force F is unchanged, but the distance d over which the rocket applies the force is varied.
1.
Derive an expression for the distance d over which the rocket’s force acts on the astronaut as a function of t , the time it takes for the astronaut to traverse the photogates.
2.
On the axes below, sketch the general shape of a graph of d vs. t .
3.
In order to make a straight line graph, what quantities could be graphed? y-axis variable: x-axis variable: