# Forces on inclined plane question

1. An object of mass m = 1 kg is initially placed on a frictionless plane, inclined by an angle θ = 30o as indicated below. How long does it take the mass to move the distance of 10 m down the incline?

2. I had a question if how I solved this is correct. I got the right answer and I wanted to make sure this was not luck. I know that we can use kinematic equations here but I tried something else....here is what I did.

3. So we know that v=(d/t) we know d = 10m and we are solving for t, so we just need v. I know the F = ma
and I know the mass and the force on the block. The force is the x-component of the gravitational force, so Fx = mgsinθ so we can write
mgsinθ = ma and we know that a = (dv/dt) so mgsinθ = m*(dv/dt) so lets divide by m and move the dt to the left side so we get
dv = gsinθ dt. Lets integrate this so v = gsinθ*t plug this in for v in the v = (d/t) equation so
t^2*g*sinθ = d
you can now solve for t and I got an answer close to the multiple choice answer. Is this correct how I solved for velocity?

-jake

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haruspex
Homework Helper
Gold Member
2020 Award
V=d/t only works for constant velocity, or if what you are after is average velocity.