For a motion in two dimensional plane, if it follows the parameter equations shown at below. Please derive the trajectory of the motion and briefly discuss what kind of motion it

X = 2t --- (i)
Y = t + 10 --- (ii)

From (i), we have, t = $\frac X2$ --- (3)

Plug (3) to (2), replace t with $\frac X2$, we get,

Y = $\frac X2$ + 10

This is a linear equation (function)

So the trajectory is linear: Y = $\frac X2$ + 10

when t = 0: X = 0 and Y = 10
t = 1: X = 2 and Y = 11
t = 2: X = 4 and Y = 12

when t = T (T is any arbitiary time)
X = 2T and Y = T + 10

The displacement of the object when t = T relative to the starting point t = 0,

D = $\sqrt{[(T+10) - 10]^2 \, + \, (2T \, - \, 0)^2}$ = $\sqrt{5T^2}$ = $\sqrt 5 T$

Average velocity, $\overline V$ = $\frac{D}{\triangle t}$ = $\frac{D}{T \, - \, 0}$ = $\frac DT$ = $\frac{\sqrt 5 T}{T}$ = $\sqrt 5$ m/s

So $\overline V$ does not depend on t.

Hence, it is constant velocy in linear motion.