To determine the work required to stop a car, we first need to calculate the car's initial kinetic energy, since the work done will be equal to this energy (as all energy will be dissipated in stopping the car).
The formula for kinetic energy (KE) is given by:
\[ \text{KE} = \frac{1}{2} m v^2 \]
where \( m \) is the mass of the car and \( v \) is its velocity.
1. Convert the velocity from km/h to m/s:
\[ 105 \text{ km/h} = 105 \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} \]
\[ 105 \text{ km/h} = 105 \times \frac{1000}{3600} \text{ m/s} \]
\[ 105 \text{ km/h} \approx 29.17 \text{ m/s} \]
2. Plug the values into the kinetic energy formula:
\[ \text{KE} = \frac{1}{2} \times 1250 \text{ kg} \times (29.17 \text{ m/s})^2 \]
\[ \text{KE} = \frac{1}{2} \times 1250 \times 851.11 \]
\[ \text{KE} = \frac{1}{2} \times 1250 \times 851.11 \]
\[ \text{KE} = 625 \times 851.11 \]
\[ \text{KE} \approx 531944 \text{ J} \]
Therefore, the work required to stop the car is approximately 531,944 joules.
Rounded to the nearest whole number, the work is:
\[ \boxed{531944 \text{ J}} \]
How much work must be done to stop a 1250 kg car traveling at 105 km/h?
Round your answer to the nearest whole number and include units.
1 answer