is the work needed to bring a car's speed from 0 to 10 km/h less than, equal to ,or more than the work needed to bring its speed from 10 to 20 km/h? if the amounts of work are different ,what is the ratio between them?
To answer this question, we need to consider the relationship between work and kinetic energy. The work done on an object is equal to the change in its kinetic energy.
Let's assume the mass of the car remains constant. The kinetic energy of an object is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity.
Now, let's calculate the work required to bring the car's speed from 0 to 10 km/h (v1) and from 10 to 20 km/h (v2), assuming the car has the same mass:
Work1 = Change in kinetic energy1 = KE2 - KE1
Work1 = (1/2) m v1^2 - (1/2) m (0)^2 (initial velocity is 0)
Work1 = (1/2) m v1^2
Work2 = Change in kinetic energy2 = KE2 - KE1
Work2 = (1/2) m v2^2 - (1/2) m v1^2
Based on these equations, we can compare the ratio of work1 to work2:
Work2/Work1 = [ (1/2) m v2^2 - (1/2) m v1^2 ] / [ (1/2) m v1^2 ]
Work2/Work1 = (v2^2 - v1^2) / v1^2
Now we can plug in the values:
v1 = 10 km/h = 10/3.6 m/s
v2 = 20 km/h = 20/3.6 m/s
Work2/Work1 = [ (20/3.6)^2 - (10/3.6)^2 ] / (10/3.6)^2
Work2/Work1 = (400/12.96 - 100/12.96) / (100/12.96)
Work2/Work1 = (350/12.96) / (100/12.96)
Work2/Work1 = 3.4028
So, the work needed to bring the car's speed from 0 to 10 km/h is equal to approximately 3.4028 times the work needed to bring its speed from 10 to 20 km/h.