If a particle's position is given by x = 10 - 15t + 4t2 (where t is in seconds and x is in meters).?

Question

Is it moving in the positive or negative direction of x just then?

Answer 1

The derivative of the equation is dx/dt = 8t - 15. Plug t into that and the sign of dx/dt will tell you the answer. The point of sign change occurs when 8t - 15 = 0, or t = 1.875. The first answer tried to give you one of the roots of the equation (points where the value of x = 0; actually they are ~0.87 and ~2.88) but the question asks about the motion (rate of change) of x, not its value..

Answer 2

It depends at what point t is at, from 0=t to t~2.45, x is negative, above that x is a ever increasing positive number