Physics EK questions

[Hexon]

hey guys, from EK physics q185:
relating to a frictionless inclined plane with theta being angle, d=total length of ramp, and h=height of ramp, m=mass of block on ramp.
if h=5m, m=5kg, theta=30 degrees and the mass starts to move from rest, how long does it take the mass to move the distance d.

now i understand that sine 30=5/d=1/2 with d=10, but i don't understand what the answer means when they say according to the distance travelled equation: d=1/2at^2, d=10, what're the steps involved where u find time?

thanks guys

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[Hexon]

If d = vot + 1/2at^2, then when vo = 0 m/s, then d = 1/2at^2
a = 5 m/s^2, so d = 1/2(5)(t^2), so 10 = 2.5t^2
4 = t^2

t = 2 seconds

Does that help?

it does a lot, have a cookie

but can you please tell me how you got the acceleration?how did you find a=5m/s^2

 

[Hexon]

ah that makes so much sense now

so to clarify, for all newtonian physical problems, the definition of acceleration is 'gsintheta'? that makes sense considering f=ma=mg(sintheta).

tell me, why would kinetic energy and potential energy equal each other when the mass starts to move?

PE = mgh = 1/2mv(f)^2

 

[MD Odyssey]

so to clarify, for all newtonian physical problems, the definition of acceleration is 'gsintheta'? that makes sense considering f=ma=mg(sintheta).

The general expression for the acceleration of an object is F = ma where F is the vector sum of all the forces on the object and m is the mass. For each problem, there may be several forces on the object, so don't try to find an expression to memorize for every type of problem. I can come up with inclined plane problems where the net force on the object is not mgsin(&#952 down the ramp.

If you want to know what the net force is, you need to draw a free-body diagram and label all the forces. From that, you can figure out with the net force is and use the equation of motion to find the acceleration.

 

[Hexon]

thanks for the help, guys