Final answer:
The mass of the car that had its speed increased from 18 m/s to 24 m/s using 190 kJ of energy is approximately 1508 kg. This is determined by using the work-energy principle which relates kinetic energy change to mass and velocity change.
Step-by-step explanation:
The energy required to change the velocity of a car can be determined using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of an object with mass m and velocity v is given by the equation KE = ½mv². Given the energy required to increase the speed of a car from 18 m/s to 24 m/s is 190 kJ, we can set up the following equation:
∆KE = KE_final - KE_initial = ½m⋅24² - ½m⋅18² = 190,000 J
The masses cancel out on the right-hand side, allowing us to solve for the mass of the car. Applying this formula:
190,000 J = ½m(24² - 18²)
190,000 J = ½m(576 - 324)
190,000 J = ½m(252)
m = 190,000 J / (126)
m = 1507.94 kg
Therefore, the mass of the car is approximately 1508 kg.