In the first second of uniformly accelerated movement, the body travels a path of 1 m, and in the second
In the first second of uniformly accelerated movement, the body travels a path of 1 m, and in the second – 2 m. Determine the path traversed by the body in the first three seconds of movement.
t1 = 1 s.
S1 = 1 m.
t2 = 2 s.
S2ʹ = 2 m.
t3 = 3 s.
S3 -?
With uniformly accelerated motion, the path of the body is expressed by the formula: S3 = V0 * t3 + a * t3 ^ 2/2.
Let us express the path for the first and second second of the movement: S1 = V0 * t1 + a * t1 ^ 2/2, S2ʹ = S2 – S1.
S2 = V0 * t ^ 2 + a * t2 ^ 2/2.
S2ʹ = V0 * t ^ 2 + a * t2 ^ 2/2 – V0 * t1 + a * t1 ^ 2/2.
2 = V0 * 2 + a * (2) ^ 2/2 – V0 * 1 – a * (1) ^ 2/2 = V0 + 3 * a / 2.
a = 2 * (2 – 1 * V0) / 3.
S1 = V0 * t1 + (2 – 1 * V0) * t1 ^ 2/3 = V0 * 1 + (2 – 1 * V0) * (1) ^ 2/3 = 1.
2 * V0 = 1.
The initial velocity of the body is V0 = 0.5 m / s.
We find the acceleration of the body by the formula: a = 2 * (2 – 1 * 0.5) / 3 = 1 m / s2.
S3 = 0.5 m / s * 3 s + 1 m / s2 * (3 s) 2/2 = 6 m.
Answer: in the first three seconds, the body passed the path S3 = 6 m.