Parametric Particle Motion Flashcards
When do we use parametric particle motion rules
When a particle has a position given by
( x(t) , y(t) )
What is the formula for speed?
|V(t)| = √ ( (dx/dt)² + (dy/dt)²
What is the formula for acceleration?
A(t) = V ’(t) = ( x”(t) , y”(t) )
What is the formula for total distance travelled
∫ √ x’(t)² + y’(t)² dt
The root of the sum of the squared derivatives
What is the parametric definition of slope?
dy/dx = y ’(t) / x ’(t) = dy/dt ÷ dx/dt
When is the particle moving left
dx/dt < 0
OR
x ’(t) is negative
When is the particle moving right?
dx/dt > 0
OR
x ’(t) is positive
When is the particle moving up
dy/dt > 0
OR
y ’(t) is positive
When is the particle moving down
dy/dt < 0
OR
y ‘(t) is negative
When does the particle’s position graph have a VERTICAL tangent?
When dx/dt = 0
When does the particles position graph have a HORIZONTAL tangent?
When dy/dt = 0
When is the particle not moving
When both dy/dt and dx/dt = 0
