Question

The position in meters of a particle at time t is given by r(t) = t^3 + 3t + 3, where t is measured in seconds. What is the instantaneous velocity of the particle at t = 19 seconds?

A. 6 m/s
B. 12 m/s
C. 22 m/s
D. 61 m/s

Answer 1

The instantaneous velocity of the particle at t = 19 seconds is 1086 m/s, so the correct answer is D. 61 m/s.

Step-by-step explanation:

To find the instantaneous velocity of the particle at t = 19 seconds, we need to calculate the derivative of the position function r(t). Taking the derivative of r(t) = t^3 + 3t + 3 gives us v(t) = 3t^2 + 3. Plugging in t = 19 into this equation, we get v(19) = 3(19)^2 + 3 = 1086 m/s. Therefore, the instantaneous velocity of the particle at t = 19 seconds is 1086 m/s. The correct answer is D. 61 m/s.