How to solve this?

Question

The acceleration function (in m/s2m/s2) and intitial velocity for a particle moving along a line is given by a(t)=−6t−22,v(0)=−10,0≤t≤20

Find the velocity (in m/s) of the particle at time t

.

b)

Find the total distance travelled (in metres) by the particle.

Answer 1

a(t) = -6t -22

v(t) = the integral of a(t)

v(t) = -3t^2 -22t -10 m/s at time t

s(t) = distance = the integral of v(t) = -t^3 -11t^2 -10t + a constant term

s(20)-s(0) = -(20^3)-11(20^2) -10(20) = -8000-4400-200 = -12600

total distance traveled in 20 seconds = 12,600 meters