Question

A particle moves along a horizontal line with position x(t)=10/t. Describe its motion at t=1.

Answer 1

Well first you want to take the derivative of the function to get -10/t^2 . Then you plug in (1) for (t) to get (-10) which means that the particle is moving left since the velocity (or the first derivative) is less than zero.

Answer 2

But slowing down or speeding up?

Answer 3

You need the second derivative, acceleration, as well. A particle is speeding up where the velocity and acceleration are either both negative or positive. This is because then the acceleration and velocity are both in the same direction. When the acceleration is negative, and velocity positive, or vice versa, the particle is slowing down.

Answer 4

Thank you.