Answer:
v = 30.15 m/s
a = 60.07 m/s2
Explanation:
Velocity is derivative of position with respect to time
[tex]v_x = x' = 3*0.25t^2 = 0.75t^2[/tex]
[tex]v_z = z' = 5*0.75t^4/2 = 1.875t^4[/tex]
Acceleration is derivative of velocity with respect to time
[tex]a_x = v_x' = 2*0.75 t = 1.5t[/tex]
[tex]a_z = v_z' = 4*1.875t^3 = 7.5t^3[/tex]
At t = 2 seconds
[tex]v_x = 0.75*2^2 = 3m/s[/tex]
[tex]v_z = 1.875*2^4 = 30m/s[/tex]
[tex]v = \sqrt{v_x^2 + v_z^2} = \sqrt{3^2 + 30^2} = \sqrt{909} = 30.15 m/s[/tex]
[tex]a_x = 1.5*2 = 3 m/s^2[/tex]
[tex]a_z = 7.5*2^3 = 60 m/s^2[/tex]
[tex]a = \sqrt{a_x^2 + a_z^2} = \sqrt{3^2 + 60^2} = \sqrt{3609} = 60.07 m/s[/tex]
