Answer : Its acceleration is, ![6.25m/s^2](https://tex.z-dn.net/?f=6.25m%2Fs%5E2)
The velocity after 5 s is, 31.25 m/s
The distance traveled by the time it reaches 50 m/s is, 200 m
Solution :
First we have to calculate the acceleration.
Formula used : ![a=\frac{\Delat v}{t}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%5CDelat%20v%7D%7Bt%7D)
where,
a = acceleration
v = change in velocity = 50 - 0 = 50 m/s
t = time = 8 s
Now put all he given values in the above formula, we get
![a=\frac{50m/s}{8s}=6.25m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B50m%2Fs%7D%7B8s%7D%3D6.25m%2Fs%5E2)
Therefore, its acceleration is, ![6.25m/s^2](https://tex.z-dn.net/?f=6.25m%2Fs%5E2)
Now we have to calculate the velocity after 5 second.
Formula used : ![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
where,
v = final velocity
u = initial velocity = 0 m/s
a = acceleration = ![6.25m/s^2](https://tex.z-dn.net/?f=6.25m%2Fs%5E2)
t = time = 5 s
Now put all the given values in the above formula, we get
![v=0m/s+(6.25m/s^2)\times (5s)=31.25m/s](https://tex.z-dn.net/?f=v%3D0m%2Fs%2B%286.25m%2Fs%5E2%29%5Ctimes%20%285s%29%3D31.25m%2Fs)
Therefore, the velocity after 5 s is, 31.25 m/s
Now we have to calculate the distance traveled by the time it reaches 50 m/s.
Formula used : ![v^2-u^2=2as](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as)
where,
s = distance traveled
Now put all the given values in the above formula, we get
![(50m/s)^2-(0m/s)^2=2\times (6.25m/s^2)\times s](https://tex.z-dn.net/?f=%2850m%2Fs%29%5E2-%280m%2Fs%29%5E2%3D2%5Ctimes%20%286.25m%2Fs%5E2%29%5Ctimes%20s)
![s=200m](https://tex.z-dn.net/?f=s%3D200m)
Therefore, the distance traveled by the time it reaches 50 m/s is, 200 m