In
the previous chapter, we have analyzed objects with
constant velocity. When the velocity of an object
changes, the object is said to be accelerated. In
this chapter, we will further analyze the motion and
think about how fast an object moves, how far it
moves and for how long.

When an object's
velocity changes, it accelerates. Acceleration shows the
change in velocity in a unit time. Velocity is
measured in meters per second, m/s, so acceleration
is measured in (m/s)/s, or m/s^{2}, which can
be both positive and negative.

The average acceleration is
the ratio between the change in velocity and the time
interval.

For example, if a car moves from the
rest to 5 m/s in 5 seconds, its average acceleration
is

An instantaneous
acceleration is the change in velocity at
one moment. We will study instantaneous acceleration
more in depth later in the chapter.

QUESTION:
If a car accelerates from 5 m/s to 15 m/s
in 2 seconds, what is the car's average
acceleration?
m/s/s

QUESTION: How
long does it take to accelerate an object
from rest to 10 m/s if the acceleration was 2
m/s^{2}?
s

QUESTION: Carl
started to run at 10 km/h when he left his
house. He arrived at school 30 minutes later.
How fast was he running when he arrived
there? Assume that his average acceleration
was 30 km/h^{2}.
km/h

In
this section, we will assume that acceleration is
always constant.

We know that the area under the line of a
velocity-time graph represents the displacement.
Therefore, the equation

is true, where V_{i}
is the initial velocity and V_{f} is the
final velocity, since the area of a triangle is 1/2 *
width * height.

QUESTION:
If a car accelerated from 5 m/s to 25 m/s
in 10 seconds, how far will it travel?
m

The final velocity of a uniformly
accelerated object is

,

where:

V_{f} is the final velocity in m/s,

V_{i} is the initial velocity in m/s,

a is acceleration in m/s^{2}, and

t is time in second.

Therefore, by substituting it to the previous
equation,

therefore, is true. If
you don't understand the derivation, don't worry. The
red formulae are the ones that you should learn.

QUESTION:
What is the displacement of a car whose
initial velocity is 5 m/s and then
accelerated 2 m/s^{2} for 10 seconds?
m

From equations and , we can also
say that

Therefore, is true.
These four red equations are very important and you
should be very familiar with them. (It doesn't mean
that you should memorize these formulae. Learn by
using them.)

QUESTION:
What is the final velocity of a car that
accelerated 10 m/s^{2} from rest and
traveled 180m?
m/s

Galileo was the first to find out that all objects
falling to Earth have a constant acceleration of 9.80
m/s^{2} regardless of their mass. Acceleration due to gravity
is given a symbol g,
which equals to 9.80 m/s^{2}.

Therefore, if you drop a pen, it should behave
like this...

Time (s)

Velocity (m/s)

Displacement (m)

0

0

0

1

9.8

4.9

2

19.6

19.6

3

29.4

44.1

4

39.2

78.4

For all previous equations, we can substitute g
for a:

QUESTION:
How long will it take for an apple
falling from a 29.4m-tall tree to hit the
ground?
s