how much work is required to make a 1400 kg car increase its speed from 10 m/s to 20 m/s?
what average force is required if the car travels 15 m during this speed change?
work = change in KE (1/2 mv^2)
10+at = 20
10t + 1/2 at^2 = 15
So would the first one be
Ke= 1/2mv2^2-1/2mv1^2
Ke= 1/2m(v2-v1)^2
Ke= 1/2(1400)(20-10)^2
Ke= 70000 J
To calculate the work required to change the speed of 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.
The formula for work is given by:
Work = 1/2 * m * (vf^2 - vi^2)
Where:
m = mass of the car = 1400 kg
vi = initial velocity = 10 m/s
vf = final velocity = 20 m/s
Substituting the given values into the formula, we have:
Work = 1/2 * 1400 kg * ((20 m/s)^2 - (10 m/s)^2)
To calculate the average force required during this speed change, we can use Newton's second law of motion, which states that force equals mass times acceleration.
The formula for force is given by:
Force = mass * acceleration
Since the car traveled a distance of 15 m, we can use the equation for acceleration:
Acceleration = (vf^2 - vi^2) / (2 * displacement)
Where displacement is the distance covered during the speed change.
Substituting the given values into the equation, we have:
Acceleration = (20 m/s)^2 - (10 m/s)^2) / (2 * 15 m)
Finally, we can calculate the force:
Force = 1400 kg * ((20 m/s)^2 - (10 m/s)^2) / (2 * 15 m)
Evaluating these calculations will give you the values of work and force required.