Question

Question attached below

Answer 1

s(8) = 1162

Explanation:

We are told that the acceleration is;

a(t) = 18t + 16

Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.

v(t) = ∫a(t) = ∫(18t + 16)

v(t) = 9t² + 16t + c

We are told that at t = 0, v(0) = 16

Thus;

9(0)² + 16(0) + c = 16

c = 16

Thus;

v(t) = 9t² + 16t + 16

Also, the velocity is the first derivative of distance. Thus;

S = ∫v(t) = ∫9t² + 16t + 16

S = 3t³ + 8t² + 16t + c

At t = 0, s(t) = 10. Thus;

10 = 3(0³) + 8(0²) + 16(0) + c

c = 10

Thus;

s(t) = 3t³ + 8t² + 16t + 10

At t = 8;

s(8) = 3(8³) + 8(8²) + 16(8) + 10

s(8) = 1162