A Train Traveling Slows Down Suddenly Stops After 20 Meters At -30 M/S^2, Prove That..., The Final Velocity Is 34.64 M/S , The Time It Requires To Sto

A train traveling slows down suddenly stops after 20 meters at -30 m/s^2

Prove that...
The final velocity is 34.64 m/s
The time it requires to stop is 1.16 seconds

 

Problem:

A train traveling slows down suddenly stops after 20 meters at -30 m/s^2

Prove that...

The final velocity is 34.64 m/s  

The time it requires to stop is 1.16 seconds

Note: it is impossible to prove that final velocity is 34.64 m/s since a train suddenly stop means final velocity is 0 m/s. But it can be proven if initial velocity is 34.64 m/s.

Given:

t (time) = 1.16 seconds

d (distance) = 20 meters

a (acceleration) = -30 m/s^2 (negative since its decelerating)

Vi (initial velocity) = ? unknown to prove 34.64 m/s

Solution:

We can use the formula d = Vit + 1/2at^2

To solve for Vi, we can use Vi = d - 1/2 at^2 / t

Vi = d - 1/2 at^2 / t

    = 20 m - 1/2 × (-30 m/s^2) × (1.16 s)^2 / 1.16 s

    = 20 m - (- 15 m/s^2 ×  1.3456 s^2 )/ 1.16 s     (cancel unit s^2)

    = 20 m -  (- 20.184  m) / 1.16 s

    =  40.184 m/ 1.16 s

    = 34.64 m/s

Answer:

velocity initial is 34.64 not velocity final.

Hope it helps...=)