14) determine when the object changes direction according to the parametric equations on t = 0, 6.\n$x(t)=5t…

Explanation:

Step1: Find the velocity - components

The velocity in the x - direction is given by $v_x=\frac{dx}{dt}$. Differentiating $x(t)=5t - 10$ with respect to $t$, we get $v_x=\frac{d}{dt}(5t - 10)=5$. The velocity in the y - direction is given by $v_y=\frac{dy}{dt}$. Differentiating $y(t) = 4$ with respect to $t$, we get $v_y=\frac{d}{dt}(4)=0$.

Step2: Analyze the velocity components

Since $v_x = 5>0$ (constant) and $v_y = 0$ (constant) for all $t\in[0,6]$, the object is moving in a straight - line in the positive x - direction and never changes direction.

Answer:

object doesn't change direction