The body, moving in a straight line with an acceleration of 5 m / s2, reached a speed of 30 m / s, and then, moving equally slowly

| November 17, 2020 | education

The body, moving in a straight line with an acceleration of 5 m / s2, reached a speed of 30 m / s, and then, moving equally slowly, stopped after 10 s. Determine the path traveled by the body.

V0 = 0 m / s.
a1 = 5 m / s ^ 2.
V1 = 30 m / s.
t2 = 10 s.
V2 = 0 m / s.
S -?
The total running time S will consist of the acceleration time S1 and the deceleration time S2: S = S1 + S2.
Find the distance traveled during acceleration: S1 = V0 * t1 + a1 * t1 ^ 2/2, where t1 is the acceleration time, a1 is the acceleration during acceleration. Since V0 = 0 m / s, then S1 = a1 * t1 ^ 2/2.
We find the acceleration time by the formula: t1 = (V1 – V0) / a1.
t1 = (30 m / s – 0 m / s) / 5 m / s ^ 2 = 6 s.
S1 = 5 m / s ^ 2 * (6 s) ^ 2/2 = 90 m.
We find the path during braking by the formula: S2 = V1 * t2 + a2 * t2 ^ 2/2, where t2 is the braking time, a2 is the acceleration during braking.
a2 = (V2 – V1) / t2.
S2 = V1 * t2 + (V2 – V1) * t2 / 2.
S2 = 30 m / s * 10 s + (0 m / s – 30 m / s) * 10 s / 2 = 150 m.
S = 90 m + 150 m = 240 m.
Answer: the path covered by the body is S = 240 m.



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