An object glides on a horizontal tabletop with a coefficient of kinetic friction of 0.3 If it comes to rest after 1.3 seconds what was its initial velocity?

Answer 1

Correct and easier way:

Kinetic friction is just a part of magnitude of forces affecting an object, so it can be multiplied by g(9.81) to get the total acceleration essentially.

Coefficient(.3)=F(friction)/F(normal)

So multiply .3 by g(9.81) to get 2.943

-2.943 is the acceleration of the object, as it's slowing down)

So then, simply multiply by time (1.3) to get a Vi of 3.8259

Ffriction = -0.3 * m * g = m * a

a = -0.3 * g

So if we integrate over time:

v(t) = -0.3 * g * t + v(0)

We know that v(t=1.3) = 0. So we can place it in the equation.

v(t=1.3) = 0 = -0.3 * g * 1.3 + v(0)

v(t=0) = 0.3*1.3*g = 0.39 * g = 0.507 meters per second