# The speed of the body is given by the equation V = 5 + 2t. Determine the path of the body in 10 s.

October 9, 2021 | education

| Given:

V (t) = 5 + 2 * t – the equation for the change in the speed of the body;

t = 10 seconds – time span.

It is required to determine S (meters) – the path that the body will cover in time t.

Let’s find the initial speed of the point:

V0 = 5 + 2 * 0 = 5 + 0 = 5 m / s.

Let’s find the acceleration of the point:

a = V (t) ‘= (5 + 2 * t)’ = 2 m / s ^ 2.

Then the path traversed by the point will be equal to:

S = V0 * t + a * t ^ 2/2 = 5 * 10 + 2 * 10 ^ 2/2 = 50 + 10 ^ 2 = 50 + 100 = 150 meters.

Answer: in 10 seconds the body will cover a distance of 10 meters.

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