A 1,500 kg car starts from rest and accelerates to a speed of 12 m/s over a distance of 68 m
a) calculate the total work on the car
b) calculate the net force that caused the car to accelerate (constant force)
To solve these problems, we need to use a few key equations from physics.
a) To calculate the total work done on the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:
Work = Change in Kinetic Energy
The change in kinetic energy is given by the formula:
Change in Kinetic Energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
b) To calculate the net force that caused the car to accelerate, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net Force = mass * acceleration
Given that the car starts from rest and reaches a final velocity of 12 m/s over a distance of 68 m, we can use the equation for average acceleration:
Acceleration = (final velocity - initial velocity) / distance
Now, let's plug in the numbers and solve the problems:
a) Total work on the car:
First, let's find the initial velocity by assuming it is 0 m/s at rest. The final velocity is given as 12 m/s. The mass of the car is 1,500 kg. The distance covered is 68 m. So, the equation becomes:
Change in Kinetic Energy = (1/2) * 1,500 kg * (12 m/s)^2 - (0 m/s)^2
Change in Kinetic Energy = (1/2) * 1,500 kg * 144 m^2/s^2
Change in Kinetic Energy = 108,000 Joules
Therefore, the total work done on the car is 108,000 Joules.
b) Net force that caused the car to accelerate:
First, let's find the acceleration using the equation mentioned earlier. The initial velocity is 0 m/s, the final velocity is 12 m/s, and the distance covered is 68 m. So, the equation becomes:
Acceleration = (12 m/s - 0 m/s) / 68 m
Acceleration = 0.1765 m/s^2
Now, we can calculate the net force using Newton's second law:
Net Force = 1,500 kg * 0.1765 m/s^2
Net Force = 264.75 Newtons
Therefore, the net force that caused the car to accelerate is 264.75 Newtons.