Question

the acceleration of a particle as it moves along a straight line is given by a=(2t-1)m/s^2, where t is in seconds.if s=1m and v= 2m/s when t=0,determine the particles velocity and position when t=6s. Also, determine the total distance the particle travels during this time period.

Answer 1

a = 2t - 1
then v = t2 - t + c
when t = 0, v = 2
2 = c
then v = t^2 - t + 2

s = (1/3)t^3 - (1/2)t^2 + 2t + k
when t = 0 , s = 1
1 = k

s = (1/3)t^3 + (1/2)t^2 + 2t + 1

plug in t=6 to get your results.