Calculus

Calculus of Parametric Equations

Parametric Equations - Velocity and Acceleration

         

Suppose the position of point P=(x(t),y(t))P=(x(t), y(t)) at time tt is given by (5t2+4,5t3+4t). \left ( 5{t}^2+4, -5{t}^3+4t \right ) . What is the magnitude of acceleration of PP at time t=5? t=5 ?

Suppose the position of point P=(x,y)P=(x, y) at time tt is given by (2t,2t2+4t). \left ( 2t, -2{t}^2+4t \right ). What is the magnitude of the velocity of PP at time t=8? t=8 ?

Suppose the position of a particle PP at time tt is given by (8etcost+2,8etsint+6).\left ( -8{e}^t\cos t + 2 , 8{e}^t\sin t + 6 \right ). What is the angle α \alpha (0<α<π0 < \alpha < \pi) between the xx-axis and the velocity vector v\vec{v} of PP at time t=π2?t= \frac{\pi}{2}?

Leaving from the origin at the same time, point PP moves at a rate of 55 cm per second in the positive direction of the xx-axis, while point QQ moves at a rate of 1010 cm per second in the positive direction of the yy-axis. What is the velocity vector v=(dxdt,dydt) \vec{v}=\left ( \frac{dx}{dt} , \frac{dy}{dt} \right ) of the intersection point between the line PQ \overline {PQ} and the line y=3xy=3x ?

Suppose the position of point P=(x(t),y(t))P=(x(t), y(t)) at time tt is given by (4t10sint,10cost+10). \left ( 4t-10\sin t, 10\cos t + 10 \right ) . What is the maximum speed attained by point P?P?

×

Problem Loading...

Note Loading...

Set Loading...