The body moves uniformly along the ОХ axis behind tau. Its speed has increased 3 times. The path is 20m. If a = 5m / s2, then what is the time
To find the duration of the body’s motion along the ОХ axis, we will use the formula: S = (V ^ 2 – V0 ^ 2) / 2a = (9V0 ^ 2 – V0 ^ 2) / 2a = 4V0 ^ 2 / a = 4V0 ^ 2 / a = 4 * (a * t / 2) ^ 2 / a = 4 * (a * t / 2) ^ 2 / a = 4 * a ^ 2 * t ^ 2 / 4a = a * t ^ 2, whence we express: t = √ (S / a); the initial speed was expressed from the formula: V = V0 + a * t = 3V0; 3V0 – V0 = a * t and V0 = a * t / 2.
Variables: S – distance traveled (S = 20 m); a – acceleration of the body (a = 5 m / s2).
Calculation: t = √ (S / a) = √ (20/5) = 2 s.
Answer: The body moved for 2 seconds.
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