Answer:
<em>(a) The average velocity is 16 m/s</em>
<em>(b) The acceleration is 0.4 m/s^2</em>
<em>(c) The final velocity is 24 m/s</em>
Explanation:
<u>Constant Acceleration Motion</u>
It's a type of motion in which the velocity (or the speed) of an object changes by an equal amount in every equal period of time.
Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, final speed is calculated as follows:
![v_f=v_o+at\qquad\qquad [1]](https://tex.z-dn.net/?f=v_f%3Dv_o%2Bat%5Cqquad%5Cqquad%20%5B1%5D)
The distance traveled by the object is given by:
![\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3Dv_o.t%2B%5Cfrac%7Ba.t%5E2%7D%7B2%7D%5Cqquad%5Cqquad%20%5B2%5D)
(a) The average velocity is defined as the total distance traveled divided by the time taken to travel that distance.
We know the distance is x=640 m and the time taken t= 40 s, thus:
![\displaystyle \bar v=\frac{x}{t}=\frac{640}{40}=16](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20v%3D%5Cfrac%7Bx%7D%7Bt%7D%3D%5Cfrac%7B640%7D%7B40%7D%3D16)
The average velocity is 16 m/s
Using the equation [1] we can solve for a:
![\displaystyle a=\frac{v_f-v_o}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Cfrac%7Bv_f-v_o%7D%7Bt%7D)
(c) From [2] we can solve for a:
![\displaystyle a= 2\frac{x-v_ot}{t^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%202%5Cfrac%7Bx-v_ot%7D%7Bt%5E2%7D)
Since vo=8 m/s, x=640 m, t=40 s:
![\displaystyle a= 2\frac{640-8\cdot 40}{40^2}=0.4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%202%5Cfrac%7B640-8%5Ccdot%2040%7D%7B40%5E2%7D%3D0.4)
The acceleration is 0.4 m/s^2
(b) The final velocity is calculated by [1]:
![v_f=8+0.4\cdot 40](https://tex.z-dn.net/?f=v_f%3D8%2B0.4%5Ccdot%2040)
![v_f=8+16=24](https://tex.z-dn.net/?f=v_f%3D8%2B16%3D24)
The final velocity is 24 m/s