A 1760 kg car accelerates uniformly from rest to 8.8 m/s in 4.52 s.
Find the work done on the car in this time.
Answer in units of J.
To find the work done on the car, we need to use the formula:
Work = Force × Distance
Since the car is accelerating uniformly, we can use Newton's second law of motion to determine the force acting on the car:
Force = Mass × Acceleration
First, let's calculate the acceleration of the car. The formula for acceleration is:
Acceleration = (Final Velocity - Initial Velocity) / Time
Given that the initial velocity (Vi) is 0 m/s, the final velocity (Vf) is 8.8 m/s, and the time (t) is 4.52 s, we can substitute these values into the equation to find the acceleration:
Acceleration = (8.8 m/s - 0 m/s) / 4.52 s
Now, calculate the acceleration.
Acceleration = 8.8 m/s / 4.52 s
Next, plug in the mass (m) and acceleration (a) values into the force equation:
Force = 1760 kg × (8.8 m/s / 4.52 s)
Calculate the force:
Force = 1760 kg × 1.9469026548672567 m/s^2
Now we have the force acting on the car. To find the work done on the car, we need to multiply the force by the distance traveled.
However, we don't have the distance, but we can find it using the kinematic equation:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)
Plugging in the values, the initial velocity (Vi) is 0 m/s, the time (t) is 4.52 s, and the acceleration (a) is the one we calculated earlier.
Distance = (0 m/s × 4.52 s) + (0.5 × 1.9469026548672567 m/s^2 × (4.52 s)^2)
Calculate the distance:
Distance = 0 + (0.5 × 1.9469026548672567 m/s^2 × 20.4304 s^2)
Now, multiply the force and distance to find the work done:
Work = Force × Distance
Work = (1760 kg × 1.9469026548672567 m/s^2) × (0.5 × 1.9469026548672567 m/s^2 × 20.4304 s^2)
Calculate the work:
Work = 1760 kg × 1.9469026548672567 m/s^2 × 0.5 × 1.9469026548672567 m/s^2 × 20.4304 s^2
Finally, you can multiply these numbers together to find the work done on the car in joules (J).