Question 877658
Acceleration is the second derivative of position and the first derivative of velocity.
Integrate with respect to time.
{{{V(t)=int(a(t),dt)=int((7t+8),dt)}}}
{{{V(t)=(7/2)t^2+8t+C}}}
Using the intial condition,
{{{V(0)=(7/2)(0)^2+8(0)+C=9}}}
{{{C=9}}}
{{{V(t)=(7/2)t^2+8t+9}}}
Integrating again with respect to t.
{{{S(t)=(7/6)t^3+4t^2+9t+C}}}
Again use the initial condition to solve for C.
{{{S(0)=(7/6)(0)^3+4(0)^2+9(0)+C=10}}}
{{{C=10}}}
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{{{S(t)=(7/6)t^3+4t^2+9t+10}}}