A 1.92 × 103 kg car accelerates uniformly from rest to 12.4 m/s in 3.77 s.
What is the work done on the car in this time interval?
work= force*distance=mass*acceleration*distance
= mass (12.4/3.77)(12.4)
To find the work done on the car, we can use the equation:
Work = Force × Distance
In this case, the force required to accelerate the car uniformly is given by Newton's second law:
Force = mass × acceleration
The acceleration can be found using the equation for uniformly accelerated motion:
acceleration = (final velocity - initial velocity) / time
Given:
- mass of the car, m = 1.92 × 10^3 kg
- initial velocity, u = 0 m/s (because the car starts from rest)
- final velocity, v = 12.4 m/s
- time, t = 3.77 s
First, calculate the acceleration:
acceleration = (v - u) / t
= (12.4 m/s - 0 m/s) / 3.77 s
= 3.285 m/s^2 (rounded to three decimal places)
Then, calculate the force:
Force = mass × acceleration
= 1.92 × 10^3 kg × 3.285 m/s^2
= 6313.2 N (rounded to three decimal places)
Finally, calculate the work done:
Work = Force × Distance
However, the distance is not given in the question. To calculate it, we can use the formula for uniformly accelerated motion:
Distance = initial velocity × time + (1/2) × acceleration × time^2
Since the car starts from rest (u = 0), the formula simplifies to:
Distance = (1/2) × acceleration × time^2
Distance = (1/2) × 3.285 m/s^2 × (3.77 s)^2
= 18.569 m (rounded to three decimal places)
Now we can calculate the work done on the car:
Work = Force × Distance
= 6313.2 N × 18.569 m
= 117,186.032 J (rounded to three decimal places)
Therefore, the work done on the car in this time interval is approximately 117,186.032 Joules.