The position x (in meters) of a particle moving along the x-axis is related to time t (in seconds) by the equation t = 3 x + 4 . The position of the particle at the instant its velocity becomes 2 m/s is:

Step-by-step solution

Given the relation between time and position: t = 3 x + 4 Differentiating both sides with respect to time t : 1 = 3 2 x d x d t Since velocity v = d x d t , we can write: 1 = 3v 2 x Rearranging for v : v = 2 x 3 We are given that the velocity v = 2 m/s. Substituting this value into the equation: 2 = 2 x 3 x = 3 Squaring both sides gives: x = 9 m Answer: 9 m