Question

You are operating a remote - controlled model car on a vacant tennis court . Your position is the origin of coordinates , and the surface of the court lies in the -plane . The car, which we represent as a point , has x- and y- coordinates that vary with time according to x = 2.0m - (0.25 m/s ^ 2) * t ^ 2; y = (1, 0 m/s) * t + (0.025 m/s ^ 2) * t ^ 2 a ) Find the car's coordinates and its distance from you at time t=2.0 s. b ) Find the car's displacement and average velocity vectors during the interval from Ostot t=2.0 s. c ) Find the components of the average acceleration in the interval from t = 0.5to; t=2.0 s. 

Answer 1

$x=2-0.25t^2,$

$y=t+0.025t^2,$

a)

$x(2)=1~m,$

$y(2)=2.1~m,$

$r=\sqrt{x^2(2)+y^2(2)}=2.33~m,$

b)

$\vec r=\vec i+2.1\vec j,$

$v_x=-0 .5t,~v_x(2)=-1~\frac ms,$

$v_y=1+0.05t,~v_y(2)=1.1~\frac ms,$

$\vec v=-\vec i+1.1\vec j,$

c)

$a_x=-0.5,$

$a_y=0.05.$