# The boy slides down the mountain on a sled, moving from a state of rest in a straight line and uniformly

**The boy slides down the mountain on a sled, moving from a state of rest in a straight line and uniformly accelerated. During the first 2 s after the start of movement, its speed increases to 3 m / s. After what time interval from the beginning of the movement will the boy’s speed become equal to 4.5 m / s? What path will he take in this period of time?**

V0 = 0 m / s.

t1 = 2 s.

V1 = 3 m / s.

V2 = 4.5 m / s.

t2 -?

S2 -?

The acceleration of a body is a vector physical quantity that shows how the velocity V changes over time t: a = (V – V0) / t.

Since the initial speed of the boy is V0 = 0 m / s, then a = V1 / t1, a = V2 / t2.

V1 / t1 = V2 / t2.

t2 = V2 * t1 / V1.

t2 = 4.5 m / s * 2 s / 3 m / s = 3 s.

The path S2 traversed by the body is determined by the formula: S2 = V0 * t2 + a * t2 ^ 2/2 = V0 * t2 + V1 * t2 ^ 2/2 * t1.

S2 = 0 m / s * 3 s + 3 m / s * (4.5 s) ^ 2/2 * 3 s = 10.125 m.

Answer: the boy will cover the path S2 = 10.125 m in time t2 = 3 s.