Newto 2nd law of motion?

Question

1. A weight,W lb,slides down an inclined plane that makes an angle alpha with the horizontal.Assume that no force other than gravity is acting on the body,that is,there is no friction,no air resistance etc.At time t=0.let the distance traveled x by x sub 0 and let the initialy velocity be v sub .Determine x for t>0

ans. x= 1/2 gt^2 sin alpha + v sub 0*t +x sub 0

please help me with the solution....i dont get this

thanks

Answer 1

Resolve the force of gravity along the line of the plane and perpendicular to it. Now the angle made by the force of gravity with the plane would be 90 - b ( b for alpha)
Therefore the component of force along the plane is WCos(90-b) or Wsin(b). This is the one that pulls the block down. The other component just results in getting a normal reaction from the plane and does not contribute to the motion along the plane.
F=ma => Wsin(b) = m * a
a = (W/m) * sin(b) = gsin(b) (since ratio of weight to mass is g)
Now apply S(t) = x(0) + v(0)t+(1/2)at^2
S = x
=> x = x(0) + v(0) * t + (1/2) * gsin(b) * t^2