It takes 214 kJ of work to accelerate a car from 23.1 m/s to 29.3 m/s. What is the car's mass?
Work = 214,000 J
= difference in kinetic energy.
= (M/2)(V2^2 - V1^2)
Solve for M (in kg)
so would it be 1/2(29.3-23.1)/214000
To find the car's mass, we can use the equation:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given that the work required is 214 kJ, the initial velocity is 23.1 m/s, and the final velocity is 29.3 m/s, we can plug in these values into the equation and solve for the mass.
First, let's convert the work from kilojoules (kJ) to joules (J) since the equation requires the unit to be in joules.
1 kilojoule (kJ) = 1000 joules (J)
So, 214 kJ = 214,000 J.
Now, let's substitute the values into the equation:
214,000 J = (1/2) * mass * (29.3^2 - 23.1^2)
Calculate the difference that is inside the parentheses:
29.3^2 - 23.1^2 = 859.21 - 533.61 = 325.6
Now we have:
214,000 J = (1/2) * mass * 325.6
To isolate the mass, we can divide both sides of the equation by (1/2) * 325.6:
mass = (214,000 J) / ((1/2) * 325.6)
Simplifying the right side:
mass = (214,000 J) / (162.8)
Dividing 214,000 J by 162.8:
mass = 1313.673 m/s
Therefore, the car's mass is approximately 1313.673 kg.