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Jake14

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**1. A**n 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 let's divide by m and move the dt to the left side so we get

dv = gsinθ dt. Let's 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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