How Do You Calculate the Velocity of a Mine Car Hoisted Up an Incline?

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SUMMARY

The discussion focuses on calculating the velocity of a 400 kg mine car being hoisted up an incline defined by a right triangle with sides 8, 15, and 17. The force in the cable is given as F=3200t^2 N, and the initial velocity is 2 m/s at t=0. By applying Newton's second law (F=ma) and integrating the acceleration, the final velocity at t=2 seconds is determined to be 14.10 m/s, confirming the calculations are accurate.

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Homework Statement


A 400kg mine car is hoisted up the incline (8,15,17 Triangle which i calculated the angle to be 28.0724 degrees)using a cable and motor. For a short time, the force in the cable is F=3200t^2 N, where t is in seconds. If the car has an initial velocity v=2 m/s @ t=0, determine its velocity @ t=2.


Homework Equations



F=ma

The Attempt at a Solution



Since there is no friction i believe that the Y forces don't matter nore does the Normal.
So I sumed the forces in the x direction which is parallel to the slope of the hill.

E F(x)=F-mgsin(theta)=ma i got a=8t^2 - 4.616...

i then integrated a to get v=8/3 t^3 - 4.616t+c c= 2. pluged in t=2 and got v=14.10 m/s


is this correct
 
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looks correct...
 

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