Finding the velocity of a vehicle.?

If you use v^2 = 2 as

then you either have v^2 = 2 ( g * sin(10) ) * 10

or v^2 = 2 * g * ( 10 * sin(10) )

which are clearly the same thing.

If you use 1/2 m v^2 = 0 + mgh ( using energy)

then divide by m

1/2 v^2 = gh

v^2 = 2gh

Which is once more exactly the same thing.

So you could do something like this.

a = g * sin(10)

s = 1/2 a t^2

t ^ 2 = 2s /a

However v = at

v^2 = a^2 t^2

now put it into t^2 = 2s/ a

v^2 = a^2 * 2s/ a

= 2s * a

= 2 s * g*sin(10)

which is once more the same thing.

No matter how you do it you must ALWAYS get exactly the same formula coming out.

There really is only one true way to do it no matter where you start from.

so to calculate v = sqrt( 2 * 10 *9.8 * sin(10 )) = 5.8 m/s

Energy Method

KE energy at the bottom = PE at the top

1/2mv^2 = mgh

v^2 = 2gh............(1)

h = 10sin(10)

= 1.736481777

= 1.74 m

Put this in (1)

v^2 = 2(9.8)(1.74)

v = 5.839863012

= 5.84 m/s

Linear Motion Method

F = ma

mgsin(10) = ma

a = gsin(10)

v^2 = u^2 + 2as

v^2 = 0 + 2as

= 2g(1.74)

v = √2(9.8)(1.74)

= 5.839863012

= 5.84 m/s