What is the initial speed of the puck launched on the ice surface if it stopped after 40 seconds?

What is the initial speed of the puck launched on the ice surface if it stopped after 40 seconds? friction coefficient against ice 0.05

t = 40 s.

g = 10 m / s2.

μ = 0.05.

V0 -?

The puck moves on the ice under the action of 3 forces: m * g – gravity, N – reaction force of the ice surface, Ffr – friction force.

Let us write 2 Newton’s law in vector form: m * a = Ftr + m * g + N.

ОХ: m * a = Ftr.

OU: 0 = N – m * g.

The friction force Ffr is expressed by the formula: Ffr = μ * N = μ * m * g.

m * a = μ * m * g.

The puck on the ice will move with acceleration a = μ * g.

a = (V0 – V) / t – definition for acceleration.

Since at the end of its movement the washer stopped V = 0 m / s, then a = V0 / t.

V0 = a * t = μ * g * t.

V0 = 0.05 * 10 m / s2 * 40 s = 20 m / s.

Answer: at the moment of launch, the washer had a speed of V0 = 20 m / s.