Differentials Parametrics

Question 2

If x= f(t) and y= f(t) how do you calculate the magnitude of velocity?

Answer 2

√ [(dy/dt)^2 + (dx/dt)^2]

Question 3

If x= f(t) and y= f(t) how do you calculate position?

Answer 3

Sub in value of t into x and y

Question 4

If x= f(t) and y= f(t) how do you calculate the direction of velocity?

Answer 4

Using values for dy/dt and dx/dt direction of velocity = tan^-1 (opp/adj) = tan^-1 (dy/dt)/(dx/dt)

Question 5

If x= f(t) and y= f(t) how do you calculate the magnitude of acceleration?

Answer 5

√ [(d2y/dt2)^2 + (d2x/d2t)^2]

Question 6

If x= f(t) and y= f(t) how do you calculate the direction of acceleration?

Answer 6

Using values for dy/dt and dx/dt direction of acceleration = tan^-1 (opp/adj) = tan^-1 (d2y/dt2)/(d2x/dt2)

Question 7

If x= f(t) and y= f(t) how do you calculate the gradient of a tangent (dy/dx) at point t?

Answer 7

dy/dx = (dy/dt) x (dt/dx) then sub in value of t.

Question 8

If x= f(t) and y= f(t) how do you calculate the stationary point?

Answer 8

dy/dx = (dy/dt) x (dt/dx) = 0 then work out value of t and sub back into x= f(t) and y= f(t).

Question 9

How do you calculate d2y/dx2 ?

Answer 9

d/dx (dy/dx) using implicit differentiation as variable is t.

Question 10

What is meant by the constraint equation?

Answer 10

Eliminate the 3rd parameter and have one equation relating x and y.

Question 11

If x= f(t) and y= f(t) (non trig fns) how do you find the constraint eqn?

Answer 11

Re-arrange both for t and equate then simpify.

Question 12

If x= f(t) and y= f(t) and they are trig fns how do you find the constraint eqn?

Answer 12

Square both sides of each equation and add together - rearrange and simplfy to eliminate trig part.

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15