Question

Two particles start at the origin and move along the x-axis.For 0t10, their respective positionfunctions are given by x1 = sin t and x2 =e-2t-1. For how many values of t do the particles havethe same velocity?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

Answer 1

There are two values of t for which the particles have the same velocity.

Step-by-step explanation:

To find the values of t for which the particles have the same velocity, we need to find the derivative of their respective position functions with respect to time. Taking the derivative of x1 = sin t, we get v1 = cos t. Taking the derivative of x2 = e-2t - 1, we get v2 = -2e-2t. Setting these velocities equal to each other, we have cos t = -2e-2t. Solving this equation, we find that there are two values of t for which the particles have the same velocity.