Learning Goal:
Suppose an object has an initial velocity v⃗ iv→i at time titi and later, at time tftf, has velocity v⃗ fv→f. The fact that the velocity changes tells us the object undergoes an acceleration during the time interval Δt=tf−tiΔt=tf−ti. From the definition of acceleration,
a⃗ =v⃗ f−v⃗ itf−ti=Δv⃗ Δt,a→=v→f−v→itf−ti=Δv→Δt,
we see that the acceleration vector points in the same direction as the vector Δv⃗ Δv→. This vector is the change in the velocity Δv⃗ =v⃗ f−v⃗ iΔv→=v→f−v→i, so to know which way the acceleration vector points, we have to perform the vector subtraction v⃗ f−v⃗ iv→f−v→i. This Tactics Box shows how to use vector subtraction to find the acceleration vector.
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