Answer:
-52 m/s²
Explanation:
[tex]a=26 m/s^2[/tex]
[tex]b=1.4 m/s^4[/tex]
Velocity is given by
[tex]v=at-bt^3[/tex]
Acceleration is given by
[tex]a_x=\dfrac{dv}{dt}\\\Rightarrow a_x=\dfrac{d}{dt}at-bt^3\\\Rightarrow a_x=a-3bt^2[/tex]
For maximum displacement we have to equate v = 0
[tex]0=at-bt^3\\\Rightarrow t=\sqrt{\dfrac{a}{b}}\\\Rightarrow t=\sqrt{\dfrac{26}{1.4}[/tex]
Substituting in the acceleration equation
[tex]a_x=26-3\times 1.4\times \sqrt{\dfrac{26}{1.4}}^2\\\Rightarrow a_x=26-3\times 1.4\times \dfrac{26}{1.4}\\\Rightarrow a_x=-52\ m/s^2[/tex]
The acceleration when maximum displacement is achieved is -52 m/s²
