The acceleration of a particle as it moves along a straight line is given by a (2t 1) m/s2, where t is in seconds. Suppose that s7 m and v 8 m/s when t0 Part A Determine the particle's velocity when t6 s Express your answer to three significant figures and include the appropriate units.

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Physics

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16 November, 15:41

The acceleration of a particle as it moves along a straight line is given by a (2t 1) m/s2, where t is in seconds. Suppose that s7 m and v 8 m/s when t0 Part A Determine the particle's velocity when t6 s Express your answer to three significant figures and include the appropriate units.

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Answers (1)

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Elliott Warner · Answer 1

v = 158 m / s

Explanation:

In this kinematic problem they give us the acceleration of the body, the position and speed of the initial moment, let's use the definition of acceleration

a = dv / dt

dv = a dt

We integrate

∫ d v = ∫ (2t + 1) dt

v = 2 (2t²) + 1t

We evaluate between the initial time t = 0 that has speed (vo) 8 m/s and the final time t with speed v

v - 8 = 4t2 + t

We already have the velocity formula as a function of time, let's calculate for t = 6 s

v = 8 + 4 6² + 6

v = 158 m / s