The dump truck, moving downhill, passed in 20 seconds. path 340m. and developed a speed of 18m / s.

| September 25, 2021 | education

The dump truck, moving downhill, passed in 20 seconds. path 340m. and developed a speed of 18m / s. Find the acceleration of the dump truck and its speed at the beginning of the slope.

t = 20 s.

S = 340 m.

V = 18 m / s.

V0 -?

a -?

With uniformly accelerated movement for a dump truck, the following formulas are valid: a = (V – V0) / t, S = V0 * t + a * t2 / 2, a = (V ^ 2 – V0 ^ 2) / 2 * S.

Let’s equate the first and third formula with each other: V – V0 / t = (V ^ 2 – V0 ^ 2) / 2 * S.

V – V0 / t = (V – V0) * (V + V0) / 2 * S.

1 / t = (V + V0) / 2 * S.

V + V0 = 2 * S / t.

V0 = 2 * S / t – V.

V0 = 2 * 340 m / 20 s – 18 m / s = 16 m / s.

a = (18 m / s – 16 m / s) / 20 s = 0.1 m / s2.

Answer: the speed of the dump truck at the beginning of the ascent was V0 = 16 m / s, it was moving with an acceleration of a = 0.1 m / s2.



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