Question

6. (09.02 MC)

An object's velocity is defined by the vector-valued function v(t)
= (In(t –2), e^(2t-t^2))
What is the acceleration vector a(t) at t(3)? (10 points)
O
01-14
O
O

Answer 1

The acceleration vector at t=3 is a(3) = (1, -2e^3).

Step-by-step explanation:

The acceleration vector can be obtained by taking the derivative of the velocity vector. Given that the velocity vector is v(t) = (ln(t-2), e^(2t-t^2)), we can differentiate each component of the vector separately. Taking the derivative of ln(t-2) with respect to t gives 1/(t-2), and taking the derivative of e^(2t-t^2) with respect to t gives (2-2t)e^(2t-t^2). Therefore, the acceleration vector a(t) at t=3 is a(3) = (1/(3-2), (2-2(3))e^(2(3)-(3^2))). Simplifying these expressions gives a(3) = (1, -2e^3).