Learning Goal: Suppose an object has an initial velocity V; at time t; and later, at time tf, has velocity of. The fact that the velocity changes tells us the object undergoes an acceleration during the time interval At = tf - ti. From the definition of average acceleration, + ΣΠ No elements selected = vf-vi tf-ti - Δύ At we see that the acceleration vector points in the same direction as the vector Av. This vector is the change in the velocity Av = vf - v₁, so to know which way the acceleration vector points, we have to perform the vector subtraction of — vi. This Tactics Box shows how to use vector subtraction to find the acceleration vector. - Figure 15 1: V > 1 of 1 √21 332 Select the elements from the list and add them to the canvas setting the appropriate attributes. i ? TACTICS BOX 1.2: Finding the acceleration vector. To find the acceleration as the velocity changes from vi to vf: (Figure 1) V 1. Draw the velocity vectors V ; and Vf and with their tails together. 2. Draw the vector from the tip of V; to the tip of of. This is Av because of = v¡ + ▲v. ΔΕ 3. Return to the original motion diagram. Draw a vector at the middle dot in the direction of Av; label it a. This is the average acceleration at the midpoint between vi and Vf. 12 Part A Below is a motion diagram for an object that moves along a linear path. The dots are separated by equal intervals and represent the position of the object at three subsequent instants. The vectors V21 and 32 show the average velocity of the object for the first and second time intervals. Draw the vector -21 and the acceleration vector a representing the change in average velocity of the object during the total time interval.