Question

A particle's distance traveled (in feet) at any time t (in seconds) is determined by the function s(t)=−5t3+25t2−t+4. Compute the particle's instantaneous acceleration at any time t. a(t)=−30t+50a(t)=−15t2+50t−1a(t)=−30​ There is not enough information to answer the question. None of these are correct. Question 4 2.5 pts A Particle's distance traveled (in feet) at any time t (in seconds) is determined by the function s(t)=3t3−13t2+2t−1. What is the particle's initial velocity (velocity at time zero)? 2 feet per second −1 feet per second −26 feet per second There is not enough information to answer the question. None of these are correct.

Answer 1

The particle's initial velocity is 2 feet per second.

Step-by-step explanation:

The initial velocity of the particle can be found by finding the derivative of the position function. Since the position function is s(t) = 3t^3 - 13t^2 + 2t - 1, the derivative will give us the velocity function. Taking the derivative of s(t), we get v(t) = 9t^2 - 26t + 2. To find the initial velocity, we can substitute t = 0 into the velocity function. Plugging in t = 0, we get v(0) = 2 feet per second.