To identify situations when position, velocity, and /or acceleration change, realizing that change can be in direction or magnitude. If an object's position is described by a function of time, r⃗ (t) (measured from a nonaccelerating reference frame), then the object's velocity is described by the time derivative of the position, v⃗ (t)=dr⃗ (t)dt, and the object's acceleration is described by the time derivative of the velocity, a⃗ (t)=dv⃗ (t)dt=d2r⃗ (t)dt2. It is often convenient to discuss the average of the latter two quantities between times t1 and t2: v⃗ avg(t1,t2)=r⃗ (t2)−r⃗ (t1)t2−t1 and a⃗ avg(t1,t2)=v⃗ (t2)−v⃗ (t1)t2−t1.