Question

A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 9, s(0) = 8, v(0) = −7

Answer 1

If you mean by a(t)=2t+9 is the acceleration function then we integrate...

v(t)=2t^2/2+9t+c where c is vo and we are told that that is -7 so

v(t)=t^2+9t-7 integrating again we get:

s(t)=t^3/3+9t^2/2-7t+c where c is the initial position which is 8 so

s(t)=t^3/3+9t^2/2-7t+8  which neatened up as

s(t)=(2t^3+27t^2-42t+48)/6