Answer:
[tex]0.594 m/s^2[/tex]
Explanation:
The acceleration is the derivative of the velocity. Therefore, we need to differentiate each component of the velocity to find the components of the acceleration first.
The velocity along the x-axis is:
[tex]v_x = 5.00 - 0.0170 t^2[/tex]
Differentiating,
[tex]a_x = -2(0.0180)t = -0.0360 t[/tex]
Similarly, the velocity along the y-axis is:
[tex]v_y = 2.00 + 0.550 t[/tex]
Differentiating,
[tex]a_y = +0.550[/tex]
So now we have the components of the acceleration; substituting t = 6.23 s, we get:
[tex]a_x = -0.0360 (6.23)=0.224 m/s^2\\a_y = 0.550 m/s^2[/tex]
And so the magnitude of the acceleration is
[tex]a=\sqrt{a_x^2+a_y^2}=\sqrt{(0.224)^2+(0.550)^2}=0.594 m/s^2[/tex]
