Question

An incline plane has Ф = 40.0° and μ k = 0.15. Starting from rest, how long will it take a 4.0 kg block to reach a speed of 12 m/s?

Answer 1

     The block on the action of two forces, the Force of Friction and the Tangential Weight. Using the Newton's Secound Law, we have:

$P_{t}-Fat=ma \\ mgsen\O-mgucos\O=ma \\ a=g(sen\O-ucos\O)$
 
     Using the Velocity Hourly Equation, we get:

$V=V_{o}+a\Delta t \\ \Delta t= \frac{V}{a}$
 
     Uniting the equations:

$\Delta t= \frac{V}{g(sen\O-ucos\O)}$
 
     Entering the unknowns:

$\Delta t= \frac{V}{g(sen\O-ucos\O)} \\ \Delta t= \frac{12}{10(sen40^o-0.15cos^o)} \\ \Delta t= \frac{12}{10(0,64-0.15x0.77)} \\ \Delta t= \frac{12}{5.27} \\ \boxed {\Delta t=2.28s}$

Obs: Approximate results

If you notice any mistake in my english, please let me know, because i am not native.