Answer to Question #253885 in Mechanics | Relativity for grey tyrant

Question

10. The equation for the velocity of an airplane slowing to a stop to the East on an airway is

𝑣⃗(𝑡) = 70𝑚/𝑠²

𝑡 − 44𝑚/𝑠³ 𝑡² . Derive the formula for its instantaneous acceleration and find the velocity when t=1s.

Answer 1

The instantaneous acceleration:

$$a=\frac{\text dv}{\text d t}=70-88t.\\\space\\ v(1)=70·1-44·1^2=26\text{ m/s}.$$