Motion problems
Last updated
Last updated
Motion Problems are all about this relationships: Moving position -> Velocity(or speed) -> Acceleration.
These terms are constantly confusing people, especially the follow parts:
Velocity is NOT the derivative of speed, but only the speed with a direction: s(t) = |v(t)|.
Velocity IS the derivative of Position: v(t) = p'(t)
Acceleration is the derivative of the Velocity: a(t) = v'(t)
Max or Min Position means Velocity = v(t) = p'(t) = 0
Max or Min Velocity means Acceleration = a(t) = v'(t) = 0
Max or Min Acceleration means a'(t) = v''(t) = p'''(t) = 0
Jump over here for Khan academy's quizzes.
Solve:
The tricky part here is the relationships: Position -> Velocity -> Acceleration
Position: p(t) = x(t)
Velocity: v(t) = x'(t)
Acceleration: a(t) = v'(t) = x''(t)
To conclude, the Max velocity should satisfy this: a(t) = 0 & a'(t) < 0
Differentiate x(t) twice and set x''(t) = 0, get t = 1.
The velocity is v(t) = x'(t)
The Acceleration is a(t) = v'(t) = x''(t) = 0, and get t=1
Substitute to v(1) = 3
Solve:
