Question

Find s(t)
a(t)=t^2-9t+4

Answer 1

So, s(t) is given by:

s(t) = (1/12)t^4 - (3/2)t^3 + 2t^2 + Ct + D

Explanation:

To find s(t) given a(t), you need to integrate a(t) with respect to t. Here, a(t) = t^2 - 9t + 4.

Integrate a(t) with respect to t to find v(t):

v(t) = ∫(t^2 - 9t + 4) dt

Now, find v(t):

v(t) = (1/3)t^3 - (9/2)t^2 + 4t + C

Where C is the constant of integration.

Next, to find s(t), you need to integrate v(t) with respect to t:

s(t) = ∫v(t) dt

Now, find s(t):

s(t) = ∫((1/3)t^3 - (9/2)t^2 + 4t + C) dt

s(t) = (1/12)t^4 - (3/2)t^3 + 2t^2 + Ct + D

Where C and D are constants of integration.

So, s(t) is given by:

s(t) = (1/12)t^4 - (3/2)t^3 + 2t^2 + Ct + D