Kinematics

Table of contents

• Misc
• Integrals
• Trick Question

Misc

• Acceleration ($m/s^2$) = $( 35 m/s^3 )t$
  • since $t$ is in seconds, the $s^3$ cancels out to become $s^2$
• Jerk ($m/s^3$) = $35 m/s^3$

Integrals

Riemann sum (little boxes and adding them up)

Graphical interpretation of integrals

• Given a constant acceleration, the velocity increases linearly (area under accel graph)

• Given linear velocity, the position increases quadratically (area under velocity graph)

  • Interpret this as area growing in squares (hence the power of two)

• Computing the Definite integral: Get area under graph

• Indefinite integral: Gets us the state function as we move up and down kinematic ladder

Trick Question

Athlete runs at 15 km/h. Athlete is 7.5 km away from finish line. Bird flies at instantaneous velocity of 30 km/h. Bird starts from athelete, flies toward finish line, and turns back toward athelete. Repeats until athelete crosses finish line.

How many km does the bird fly?

If we tried drawing kinematic graphs, it would be tricky because toward the end, the bird would be oscillating very quickly between the athlete and finish line.

Zeno’s Dichotomy paradox (sometimes mixed with the Achilles and the Tortoise paradox) says that to reach a finish line, you must first get halfway there, then half of the remaining distance, then half of that, and so on. Since there are infinitely many halfway points, Zeno argued that motion should be impossible.

Answer: 7.5 km in 15 km/h = 0.5 h. Bird flies at 30 km/h for 0.5 h = 15 km.