The position of an object at time t is given by the parametric equations; x=3t^2+1t, y=5t^2+6 Fine the horizontal velocity, the vertical velocity, and the speed at the moment where t=3.

Answer 1

The horizontal direction is "x" so the horizontal velocity is dx/dt = 6t + 1

The vertical direction is "y" so the vertical velocity is dy/dt = 10t

At t = 3, the value of the horizontal velocity is 6(3) + 1 = 19

At t = 3, the value of the vertical velocity is 10(3) = 30

The speed is the magnitude of the combined vector = √(19² + 30²) = 35.51