As we know that it is given to us
[tex]x = (\frac{1}{2}t^3 - 2t^2)[/tex]
[tex]y = (\frac{1}{2}t^2 - 2t)[/tex]
now we know that rate of change in position is known as velocity
so here we will have
[tex]v_x = \frac{dx}{dt}[/tex]
[tex]v_x = \frac{3}{2}t^2 - 4t[/tex]
similarly
[tex]v_y = \frac{dy}{dt}[/tex]
[tex]v_y = t - 2[/tex]
now we have t = 4.5 s
[tex]v_x = 1.5(4.5)^2 - 4(4.5) = 12.375 m/s[/tex]
[tex]v_y = 4.5 - 2 = 2.5 m/s[/tex]
now the net speed is given as
[tex]v^2 = v_x^2 + v_y^2[/tex]
[tex]v^2 = 12.375^2 + 2.5^2 [/tex]
[tex]v = 12.625 m/s[/tex]
