Answer:
(a) The average velocity is 16 m/s
(b) The acceleration is 0.4 m/s^2
(c) The final velocity is 24 m/s
Explanation:
Constant Acceleration Motion
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:
[tex]v_f=v_o+at\qquad\qquad [1][/tex]
The distance traveled by the object is given by:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]
(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:
[tex]\displaystyle \bar v=\frac{x}{t}=\frac{640}{40}=16[/tex]
The average velocity is 16 m/s
Using the equation [1] we can solve for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
(c) From [2] we can solve for a:
[tex]\displaystyle a= 2\frac{x-v_ot}{t^2}[/tex]
Since vo=8 m/s, x=640 m, t=40 s:
[tex]\displaystyle a= 2\frac{640-8\cdot 40}{40^2}=0.4[/tex]
The acceleration is 0.4 m/s^2
(b) The final velocity is calculated by [1]:
[tex]v_f=8+0.4\cdot 40[/tex]
[tex]v_f=8+16=24[/tex]
The final velocity is 24 m/s
