Our last quantity, acceleration, can also be discussed in terms of a vector acceleration or simply the magnitude, but for acceleration we have no special term for the magnitude. If we are considering instantaneous velocity, then speed is the magnitude of velocity. We discussed velocity, a vector, and speed, a scalar. For motion in one direction, distance is the magnitude of displacement. For instance, we discussed displacement, a vector, and distance, a scalar. Each one can be discussed in terms of a vector concept (magnitude and direction) or in terms of a scalar concept (magnitude only). So far, we have introduced three different aspects of motion. It is important to discuss one problem with the specialized vocabulary of physics. Each of these cases correspond to negative acceleration. This time, however, points to the right of the vertex have negative slope that is growing steeper as time goes on, and points to the left of the vertex have positive slope that is lessening. The position versus time for a system experiencing constant negative acceleration is shown below.Īgain, the vertex is a point with zero velocity. The case of a concave down position versus time graph is analogous. This lessening of a negative velocity also corresponds to positive acceleration. Everywhere to the left of the vertex, the velocity is negative and approaching zero (becoming smaller in magnitude). Thus, the velocity is increasing in the positive direction, implying positive acceleration. Everywhere to the right of the vertex in the graph, the slope of the parabola is positive and increasing. Thus, the system is momentarily at rest at the time corresponding to the vertex of the parabola. time graph implies that the velocity goes to zero at that time. The vertex of this parabola is a point where the slope of the graph goes to zero. The position versus time graph for such a system will be an upward-opening parabola like that shown below. The reason can be seen by considering the case of a system with constant positive acceleration.

A concave up position versus time graph has positive acceleration. The concavity (or equivalently, the second derivative) of a position versus time graph can be used to determine the sign of the acceleration.

Change the acceleration, position, and velocity of the man and observe the corresponding motion and motion graphs. Simulation courtesy PhET Interactive Simulations

Implies that a system moving with constant acceleration will be described by a parabolic position versus time graph (the position is a quadratic function of the time). Thus, if the acceleration is constant, the velocity versus time graph will necessarily be linear (the only type of graph with a constant slope).Īnother way to graphically represent the Model is to note that the equation It is clear that the acceleration is equal to the slope of the velocity versus time graph. One way to represent a system described by the One-Dimensional Motion with Constant Acceleration Model graphically is to draw a velocity versus time graph for that system.

Given a position versus time graph illustrating 1-D motion with constant acceleration, find any time intervals over which the object is decelerating.

Describe the conditions on velocity and acceleration that give rise to deceleration.

Given a position versus time graph illustrating 1-D motion with constant acceleration, determine the sign of the acceleration.

Given a velocity versus time graph illustrating 1-D motion with constant acceleration, determine the acceleration.

Recognize or construct a position versus time graph illustrating 1-D motion with constant acceleration.

Recognize or construct a velocity versus time graph illustrating 1-D motion with constant acceleration.

After working through this module, you should be able to:

Decelerate definition