A particle is moving with acceleration a(t)=36t+16. its position at time t=0 is s(0)=17 and its velocity at time t=0 is v(0)=2. What is its position at time t=5?

Answer 1

a(t)=36t+16. its position at time t=0 is s(0)=17 and its velocity at time t=0 is v(0)=2

If a(t)=36t+16, then v(t)=18*t^2+16*t+c, since a is the derivative of v

v(0)=18*0^2+16*(0)+c=c=2, so v(t)=18*t^2+16*t+2

s(t)=6*t^3+8*t^2+2t+c, since v is the derivative of s

s(0)=6*0^3+8*0^2+2*0+c=c=17, so s(t)=6*t^3+8*t^2+2t+17

s(5)=6*5^3+8*5^2+2*5+17=6*125+8*25+10+17=750+200+10+17=977