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. If s = 1m and v = 2m/s when t = 0, determine the particle's velocity and position when
t = 6s. Also, determine the total distance the particle travels during this time period.​

Answer 1

Answer:

d^2x/dt^2 = 2 t - 1

dx/dt = t^2 - t + c

at t = 0, dx/dt = 2 so c = 2

so

v = dx/dt = t^2 - t + 2

x = (1/3) t^3 - (1/2) t^2 + 2 t + c

when t = 0 x = a so c = 1

x = (1/3) t^3 - (1/2) t^2 + 2 t + 1

so at t = 6

v = 36 -6 + 2 = 32 m/s

and

x = 67

total distance = 67-1 = 66

assuming x is always positive (sure looks that way