Moving rectilinearly equidistantly, the body at the initial moment of time had a velocity v0 = 0.40 m / s. During the fifth second, it covered the path 5 = 0.31 m. Find the body’s acceleration modulus and the path traveled by the body to stop.
V0 = 0.4 m / s.
V = 0 m / s.
S5 = 0.31 m.
t4 = 4 s.
t5 = 5 s.
The path S5 that the body covered in the fifth second of its deceleration can be expressed by the formula: S5 = S2 – S1, where S2 is the path of the body during the time t5 = 5 s, S1 is the path of the body during the time t4 = 4 s.
With equal slow motion, the path is expressed by the formulas: S1 = V0 * t4 – a * t4 ^ 2/2, S2 = V0 * t5 – a * t5 ^ 2/2.
S5 = S2 – S1 = V0 * t5 – a * t5 ^ 2/2 – V0 * t4 + a * t4 ^ 2/2 = V0 * (t5 – t4) + a * (t4 ^ 2 – t5 ^ 2) / 2.
a = 2 * (S5 – V0 * (t5 – t4)) / * (t4 ^ 2 – t5 ^ 2).
a = 2 * (0.31 m – 0.4 m / s * (5 s – 4 s)) / * ((4 s) ^ 2 – (5 s) ^ 2) = 0.02 m / s2.
The path to the complete stop of the body S is expressed by the formula: S = (V02 – V2) / a.
S = ((0.4 m / s) ^ 2 – (0 m / s) ^ 2) / 0.02 m / s2 = 8 m.
Answer: the modulus of acceleration is a = 0.02 m / s2, the body will travel a path S = 8 m until it comes to a complete stop.
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