Acceleration

It is commonly understood that acceleration is associated with changes in speed. Although this is true, it is only part of the concept of acceleration. Suppose that during some time interval, a ball reverses its direction of motion but its initial and final speeds are equal. The quantity "change in speed" would not reflect the fact that the ball was struck by a bat. In physics we must broaden the concept of acceleration to include such cases. We say that a body accelerates when its velocity changes in magnitude or in direction, or both. The average acceleration for a finite time interval is defined as

Average acceleration = Change in velocity / Time interval

Average acceleration is a vector quantity whose direction is the same as that of the change in velocity. For one-dimensional motion, the average acceleration is

(2.6)

The SI unit of acceleration is m/s². If a car goes from rest to 90 km/h in 15 s, a = (90 km/h)/(15s) = 6 km·h^-1/s. This means that on average the velocity increases by 6 km/h in each 1-s interval. On a graph of υ versus t, such as Fig. 2.6, the average acceleration is found from the slope of the line joining the initial and final points. The sign of a _av is determined by the sign of ∆υ.

By analogy with Eqs. 2.4 and 2.5, the instantaneous acceleration is defined as the derivative of υ with respect to t:

FIGURE 2.6

(2.7)

Graphically, the instantaneous acceleration at a particular instant is found from the slope of the tangent to the υ versus t graph at that instant, as shown in Fig. 2.6. Positive acceleration points in the direction ofthe +x axis, while nega­tive acceleration points in the opposite direction. Do not assume that a negative acceleration means a deceleration. The word "deceleration" means only a slow­ing down; it tells us nothing about direction. When υ and a have the same sign, the body speeds up; when they have opposite signs, the body slows down.

Дата добавления: 2014-01-05