You are driving down the road and hit a bump which causes your fishing tackle
box to bounce out of the bed of your pickup. the box decelerates at a rate of 3
m/s and skids 24 meters before coming to a stop. how fast were you traveling
when the box fell out?

speed
=
12

m/s

Explanation:
We're asked to find the initial velocity of the box, given it constantly accelerated at
−
3

m/s
2
for
24

m
before coming to a stop.
To do this, we can use the equation
(
v
x
)
2
=
(
v
0
x
)
2
+
2
a
x
(
Δ
x
)
−−−−−−−−−−−−−−−−−−−−−−
where
v
x
is the final velocity of the box (which is
0
since it came to rest)

v
0
x
is the initial velocity of the box (what we're trying to find)

a
x
is the acceleration of the box, given as
−
3

m/s
2
(negative because it's directed opposite to motion; i.e. it is decelerating)

Δ
x
is the distance traveled by the box, given as
24

m

Plugging in knonw values, we have
0
=
(
v
0
x
)
2
+
2
(
−
3
l
m/s
2
)
(
24
l
m
)

v
0
x
=
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣

12
l
m/s

∣
∣
−−−−−−−−−−−−
The truck was thus traveling at a speed of
12

m/s
.