## Water Barrels

A car in the shown diagram collides into the water barrels typically found on highways. The barrels act as a spring to reduce impact and deflect 2 meters. If the car weighs 100 kg, and the barrels have a spring constant of 25 kN/m, what is the velocity (m/s) of the car right before impact with the wall?

##
__
__**Hint**

**Hint**

The spring’s potential energy:

$$$U=\frac{kx^{2}}{2}$$$

where
$$k$$
is the spring constant, and
$$x$$
is the compressed distance.

##
__
__**Hint 2**

**Hint 2**

The car’s kinetic energy:

$$$KE=\frac{1}{2}mv^2$$$

where
$$m$$
is the mass, and
$$v$$
is the velocity.

The spring's potential energy:

$$$U=\frac{kx^{2}}{2}=\frac{25kN\cdot (2m)^2}{m\cdot 2}=50kN\cdot m=50,000\:N\cdot m$$$

where
$$k$$
is the spring constant, and
$$x$$
is the compressed distance. The car's kinetic energy:

$$$KE=\frac{1}{2}mv^2=\frac{1}{2}(100kg)v^2=50kg\cdot v^2$$$

where
$$m$$
is the mass, and
$$v$$
is the velocity. Because energy is conserved,
$$U=KE$$
:

$$$50kg\cdot v^2=50,000N\cdot m$$$

$$$v=31.62\:m/s$$$

31.62 m/s