Question

A particle moves along the curve y=1/3x^3+2 where x and y are in meters.When x=.8, the x component of the velocity is 10m/s what is the total velocity

Answer 1

$$\frac{dy}{dx}=x^2$$

$$\frac{dy}{dt} =\frac{dy}{dx} \frac{dx}{dt} =x^2 \frac{dx}{dt}$$

$$\frac{dy}{dt} (0.8)=0.8^2(10)=6.4 \frac{m}{s}$$

Total velocity:

$$(10, 6.4) \frac{m}{s}$$