#Calculate moment of inertia of t beam how to

Thus, the zeros of the velocity function give the minimum and maximum of the position function.įigure 3.7 The object starts out in the positive direction, stops for a short time, and then reverses direction, heading back toward the origin.

If the position function had a minimum, the slope of the position graph would also be zero, giving an instantaneous velocity of zero there as well. At other times, t 1, t 2 t 1, t 2, and so on, the instantaneous velocity is not zero because the slope of the position graph would be positive or negative. The slope of the position graph is zero at this point, and thus the instantaneous velocity is zero. The instantaneous velocity is shown at time t 0 t 0, which happens to be at the maximum of the position function. Figure 3.6 shows how the average velocity v – = Δ x Δ t v – = Δ x Δ t between two times approaches the instantaneous velocity at t 0. The instantaneous velocity at a specific time point t 0 t 0 is the rate of change of the position function, which is the slope of the position function x ( t ) x ( t ) at t 0 t 0. Like average velocity, instantaneous velocity is a vector with dimension of length per time. After inserting these expressions into the equation for the average velocity and taking the limit as Δ t → 0 Δ t → 0, we find the expression for the instantaneous velocity: To find the instantaneous velocity at any position, we let t 1 = t t 1 = t and t 2 = t + Δ t t 2 = t + Δ t. The expression for the average velocity between two points using this notation is v – = x ( t 2 ) − x ( t 1 ) t 2 − t 1 v – = x ( t 2 ) − x ( t 1 ) t 2 − t 1. To illustrate this idea mathematically, we need to express position x as a continuous function of t denoted by x( t). It is the average velocity between two points on the path in the limit that the time (and therefore the displacement) between the two events approaches zero.

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity, usually called simply velocity. This section gives us better insight into the physics of motion and will be useful in later chapters. We can find the velocity of the object anywhere along its path by using some fundamental principles of calculus. However, since objects in the real world move continuously through space and time, we would like to find the velocity of an object at any single point.

#Calculate moment of inertia of t beam how to

We have now seen how to calculate the average velocity between two positions.

Calculate the speed given the instantaneous velocity.

Calculate the instantaneous velocity given the mathematical equation for the velocity.

Describe the difference between velocity and speed.

Explain the difference between average velocity and instantaneous velocity.

By the end of this section, you will be able to: