# What is the value of the initial velocity of a body if its movement occurs according to the law x = 15 + 3t + 4t ^ 2 (m)?

September 27, 2021 | education

| Given:

x (t) = 15 + 3 * t + 4 * t ^ 2 – the equation of body motion.

It is required to determine the initial velocity of the body v0.

General view of the body motion equation:

x (t) = x0 + v0 * t + a * t ^ 2/2, where:

x0 is the initial coordinate, v0 is the initial velocity, a is the acceleration of the body.

Substituting the value from the first equation into the second, we get that:

x0 = 15 meters, v0 = 3 m / s, a = 8 m / s ^ 2.

Answer: the initial speed is 3 m / s.

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