The working speed of the table of the planer metal-cutting machine reaches 30m / min after accelerating it during idle at a distance of 0.18m. Determine the acceleration time and the acceleration with which the table was moving.
These tasks: V (working speed of the table of the used planing machine) = 30 m / min = 0.5 m / s; V0 (initial speed) = 0 m / s; S (distance traveled by the planer at idle speed) = 0.18 m.
1) Acceleration time of the machine to working speed: S = (V + V0) * t / 2 and t = 2S / (V – V0) = 2 * 0.18 / (0.5 – 0) = 0.72 s.
2) Acceleration of the planer: a = (V – V0) / t = (0.5 – 0) / 0.72 = 0.694 m / s2.
Check: S = (V ^ 2 – V0 ^ 2) / 2a = (0.5 ^ 2 – 0 ^ 2) / (2 * 0.694) = 0.18 m (correct).
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