# A material point, moving uniformly accelerated without an initial speed, acquired a speed of 2 m / s

**A material point, moving uniformly accelerated without an initial speed, acquired a speed of 2 m / s in 1 s. how long will it take now to cover the path of 4m, moving with this initial speed and the same acceleration**

Given:

t = 1 second – time interval;

v = 2 m / s – the speed that the material point acquired during the time t;

S = 4 meters – the path taken by the material point after gaining speed.

It is required to determine how long t1 (second) a material point takes to cover the path S.

Let’s find the acceleration of the material point:

a = v / t = 2/1 = 2 m / s ^ 2.

Then:

S = v * t1 + a * t1 ^ 2/2;

4 = 2 * t1 + 2 * t1 ^ 2/2;

4 = 2 * t1 + t1 ^ 2;

t1 ^ 2 + 2 * t1 – 4 = 0;

D = 2 ^ 2 + 4 * 4 = 4 + 16 = 20, D ^ 0.5 = 20 ^ 0.5 = 4.5.

t11 = (-2 + 4.5) / 2 = 2.5 / 2 = 1.25, t12 = (-2 – 4.5) / 2 = -6.5 / 2 = -3.25.

t12 does not fit according to the condition of the problem (since the time cannot be negative).

Answer: the body will travel 4 meters in 1.25 seconds.