# The trolley in the mine is moving at a speed of 26 km / h. The braking force is half the force of gravity

**The trolley in the mine is moving at a speed of 26 km / h. The braking force is half the force of gravity. What path will the trolley take from the start of braking to a complete stop?**

V0 = 26 km / h = 7.2 m / s.

V = 0 m / s.

g = 10 m / s2.

Ftorm = Fт / 2.

S -?

Since in the horizontal direction only the braking force Fstorm acts, then Newton’s 2 law will have the form: m * a = Fstorm.

According to the condition Ftorm = Ft / 2, and the force of gravity is determined by the formula: Ft = m * g.

m * a = m * g / 2.

a = g / 2.

With uniformly accelerated motion, the traversed path S is found by the formula: S = (V0 ^ 2 – V ^ 2) / 2 * a.

S = (V0 ^ 2 – V ^ 2) 2/2 * g = (V0 ^ 2 – V ^ 2) / g.

S = ((7.2 m / s) ^ 2 – (0 m / s) ^ 2) / 10 m / s2 = 5.2 m.

Answer: the trolley will cover the path S = 5.2 m until it comes to a complete stop.