Acceleration vector

Force, displacement, and velocity are vectors so it should be no surprise that acceleration is also a vector. Objects may accelerate and change their velocity in any direction, x, y, or z, including any combination of ax-, ay-, or az-component accelerations. Acceleration is the change in velocity over the change in time. Read the text aloud
(6.5) a = Δ v Δt
a  = acceleration (m/s2)
Δv  = change in velocity (m/s)
Δt  = change in time (s)
Acceleration
vector definition
This equation is really shorthand for three component equations, one for each direction.
a = Δ v Δt reallymeans a x = Δ v x t , a y = Δ v y t , a z = Δ v z t
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The acceleration vector can be difficult to understand because it represents the rate of change in the velocity vector—which itself represents the rate of change in the position vector. Consider the following two cases of constant acceleration where the acceleration vector points in a different direction from the velocity. Read the text aloud
What does the motion look like if an object has an acceleration in one direction but not in another? In the example on the lower left, the initial velocity is equal to v = (0, 10) m/s north, while the acceleration vector points due east at a = (1, 0) m/s2. After one second, the velocity vector equals v = (1, 10) m/s; after two seconds, v = (2, 10) m/s. Notice that the y-component of the velocity stays the same, because there is no acceleration in the y-direction! This means that the speed is slowly increasing and the direction is turning more to the east every second. Read the text aloud
show the velocity vector as it is accelerated
In a more realistic scenario, the car starts with the same velocity v = (0, 10) m/s, but it slows down while turning (above right). The acceleration a = (1,−2) m/s2 acts to slow the car down in the y-direction. After one second the velocity is v = (1, 8) m/s, while after two seconds v = (2, 6) m/s. Notice that the y-component of the velocity decreases by 2 m/s each second. The speed decreases over time and the direction changes. Read the text aloud
The illustration above depicts the motion using both graphical and vector models. Do you find that one is one more informative than the other? Read the text aloud
For the car that is slowing down while turning, what is its velocity after 5 s? What is its speed? Show

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