Question

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.

Answer 1

Answer:

 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