Calculus when is the particle moving to the left

When is the particle speeding up? When is it slowing down? Thanks so much! JohnD It really helps readability if you format your questions using MathJax. Have a got your equation correct? Also, what have you tried and where are you confused? If this is HW, it should be tagged as such. Each question is one liner if use definition. Add a comment. Active Oldest Votes. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.

Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 3. Hot Network Questions. Question feed. Mathematics Stack Exchange works best with JavaScript enabled. By stating that a vehicle is moving at 60 miles per hour, we are really referring to the rate of motion in relation to the surface the vehicle is traveling on.

Thus, the speed of an airplane is its motion in relation to the air and that of a ship is its motion in relation to the water. In light of the fact that particle motion requires a frame of reference, we will utilize the coordinate axes and four key ideas:.

Position determines where a particle or object is located on the x-axis at a given time and is denoted by s t or x t.

Velocity determines how fast the position is changing at time t and gives the direction of movement. Acceleration determines how fast the velocity is changing at time t and shows if the velocity increases or decreases.

Velocity is a vector that has magnitude and direction, but speed is a scalar number that expresses the absolute speed of an object. Speed indicates how fast an object is moving, but velocity represents speed in a given direction. Therefore, if s t represents the position of a particle along the x-axis at any time t, then the following terms are of importance to our understanding of motion.

Because when the velocity is positive, the particle moves toward the right, and when the velocity is negative, the particle moves toward the left. If we test for either positive or negative values on either side of our critical numbers, we will be able to determine when the particle is moving right or left!

So, all we have to do is find our local extrema to determine if the particle changes direction! We do this by taking the second derivative of the position function, which is nothing more than the derivative of the velocity. First, we must find when the acceleration is at rest, so we set the acceleration function equal to zero.