Answer :
The problem asks for the kinetic energy of a car with a mass of [tex]$450\,\text{kg}$[/tex] traveling at [tex]$108\,\text{km/h}$[/tex]. The kinetic energy ([tex]$E_c$[/tex]) is given by the formula
[tex]$$
E_c = \frac{1}{2} m v^2,
$$[/tex]
where:
- [tex]$m$[/tex] is the mass,
- [tex]$v$[/tex] is the speed in meters per second.
Step 1: Convert the Speed
The given speed is in kilometers per hour. We convert [tex]$108\,\text{km/h}$[/tex] to meters per second using the conversion factor:
[tex]$$
1\,\text{km/h} = \frac{1000\,\text{m}}{3600\,\text{s}}.
$$[/tex]
Thus, the speed in meters per second is
[tex]$$
v = 108\,\text{km/h} \times \frac{1000\,\text{m}}{3600\,\text{s}} = 108 \times \frac{5}{18}\,\text{m/s} = 30\,\text{m/s}.
$$[/tex]
Step 2: Calculate the Kinetic Energy
Substitute the values into the kinetic energy formula:
[tex]$$
E_c = \frac{1}{2} \times 450\,\text{kg} \times (30\,\text{m/s})^2.
$$[/tex]
First, calculate the square of the speed:
[tex]$$
(30\,\text{m/s})^2 = 900\,\text{m}^2/\text{s}^2.
$$[/tex]
Now substitute back:
[tex]$$
E_c = \frac{1}{2} \times 450 \times 900.
$$[/tex]
Perform the multiplication:
[tex]$$
\frac{1}{2} \times 450 = 225,
$$[/tex]
so
[tex]$$
E_c = 225 \times 900 = 202500\,\text{Joules}.
$$[/tex]
Final Answer:
The kinetic energy of the car is
[tex]$$
\boxed{202500\,\text{J}}.
$$[/tex]
[tex]$$
E_c = \frac{1}{2} m v^2,
$$[/tex]
where:
- [tex]$m$[/tex] is the mass,
- [tex]$v$[/tex] is the speed in meters per second.
Step 1: Convert the Speed
The given speed is in kilometers per hour. We convert [tex]$108\,\text{km/h}$[/tex] to meters per second using the conversion factor:
[tex]$$
1\,\text{km/h} = \frac{1000\,\text{m}}{3600\,\text{s}}.
$$[/tex]
Thus, the speed in meters per second is
[tex]$$
v = 108\,\text{km/h} \times \frac{1000\,\text{m}}{3600\,\text{s}} = 108 \times \frac{5}{18}\,\text{m/s} = 30\,\text{m/s}.
$$[/tex]
Step 2: Calculate the Kinetic Energy
Substitute the values into the kinetic energy formula:
[tex]$$
E_c = \frac{1}{2} \times 450\,\text{kg} \times (30\,\text{m/s})^2.
$$[/tex]
First, calculate the square of the speed:
[tex]$$
(30\,\text{m/s})^2 = 900\,\text{m}^2/\text{s}^2.
$$[/tex]
Now substitute back:
[tex]$$
E_c = \frac{1}{2} \times 450 \times 900.
$$[/tex]
Perform the multiplication:
[tex]$$
\frac{1}{2} \times 450 = 225,
$$[/tex]
so
[tex]$$
E_c = 225 \times 900 = 202500\,\text{Joules}.
$$[/tex]
Final Answer:
The kinetic energy of the car is
[tex]$$
\boxed{202500\,\text{J}}.
$$[/tex]
