Find parametric equations that describe the circular path of the following object. Assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time given in the description. A go-cart moves counterclockwise with constant speed around a circular track of radius 300 m, completing one lap in 1.7 min. Assume the center of the track is at the origin and that the go-cart starts at (300 comma 0). What are the parametric equations?

the parametric equations for the circular path are

x = 300 m * cos (3.695 min⁻¹ t)

y = (-300 m) * sin (3.695 min⁻¹ t)

Step-by-step explanation:

the parametric equations of the go-kart are

x = R*cos (ω*t)

y = R*sin (-ω*t) = - R*sin (ω*t) (since the rotation is counterclockwise)

where R = radius, ω = angular velocity, x₀ and y₀ are the initial position in the x - axis and y - axis respectively and the parameter t = time (in minutes)

since

R = 300 m

ω = 2π / 1.7 min = 3.695 min⁻¹

therefore the equations for the circular path are

x = 300 m * cos (3.695 min⁻¹ t)

y = (-300 m) * sin (3.695 min⁻¹ t)