Question

A particle moves along the x-axis so that at any time t is greater than or equal to 0 its position is given by x(t)=(1/2)(a-t)^2 where a is positive constant. For what values of t is the particle moving to the right?

Answer 1

The particle is moving to the right for values of t less than the positive constant a.

Step-by-step explanation:

The particle is moving to the right when its velocity is positive. To determine the values of t for which the particle is moving to the right, we need to find the values of t when the velocity is positive.

The velocity function is the derivative of the position function. In this case, the position function is x(t) = (1/2)(a-t)^2 and the velocity function is v(t) = -2(a-t). We know that v(t) > 0 when -2(a-t) > 0. Solving this inequality, we find that t < a. Therefore, the particle is moving to the right for values of t less than the positive constant a.