The acceleration of a particle as it moves along a straight line is given by a = (2t – 1) m/s2. if s = 1 m and v = 2 m/s when t = 0, determine the particle’s velocity and position when t = 6 s. also determine the total distance the particle travels during this time period.

1) Velocity at t =6 =32m/s

2) Position of particle at t = 6 secs = 67 meters

3) Distance covered in 6 seconds equals 72 meters.

Explanation:

By definition of acceleration we have

Now at t = 0 v = 2 m/s thus the value of constant is obtained as

thus velocity as a function of time is given by

Similarly position can be found by

The value of constant can be obtained by noting that at time t = 0 x = 1.

Thus we get

thus position as a function of time is given by

Thus at  t = 6 seconds we have

The path length can be obtained by evaluating the integral

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