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.