Whew! Long weekend. Unfortunately, due to work/procrastination the post I wanted to write still isn’t ready. But today I’m also teaching 1d accelerated motion to my Physics 218 students, and that’s interesting of itself.
One of the things I try to do is give problems that help build instinct for what an answer should look like. If an accounting students calculates that a million-dollar-per-year business owes a billion dollars in taxes, he will instantly recognize that there’s an error somewhere. You’ve got to built up the same kind of intuition in physics. Example:
The New Horizons mission to Pluto travels at a constant(ish) speed of about ten miles per second and will take around nine years to reach its destination. If you could travel at a constant acceleration equal to the acceleration due to gravity at the earth’s surface (a = 9.8 m/s^2), how long would it take you to travel from Earth to Pluto, starting from rest? (Assume the distance to Pluto is 6×10^9 km)
Ignoring all the obvious effects and treating it as a 1-dimensional motion problem, give it a shot!
The equation for distance traveled under accelerated motion assuming a zero starting speed is:
Unfortunately chemical reactions can’t generate large constant acceleration for very long before the fuel runs out. Future advances such a nuclear propulsion, solar sails, and ion engines might help fix this.