A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 7, s(0) = 9, v(0) = −4

Answer 1

v(t) = ∫(2t + 7)dt = t² + 7t + C. v(0) = C = -4, so C = -4 and v(t) = t² + 7t - 4;

s(t) = ∫(t² + 7t - 4)dt = t³/3 + 7t²/2 - 4t + N; s(0) = N = 9.

So s(t) = t³/3 + 7t²/2 - 4t + 9

Answer 2

Hi Kaitlyn,

this problem can be solved by taking the derivative of a(t).

For physics

a(t) = v'(t) and v'(t) = s"(t)

this is called an initial value problem.

Step 1: identify that v'(t) = 2t + 7

Step 2: integrate v'(t) to get v(t), and then a C will appear

Step 3: plug in the value for v(0) = -4 into this new equation to get the C value

Step 4: identify that s'(t) = v(t) =new equation

Step 5: integrate s'(t) to get s(t) with a different constant C.

Step 6: solve for this new C value using s(t)

Step 7: rewrite the equation in terms of s(t) which is the position of the particle at any t value.

Let me know if you have anymore questions.