Is the work needed to bring a car's speed from o to 10km/h less than, egaul to or morethen the worked needed to bring its speed from 10 to 20km/h. If the amounts of work are different, what is the ratio between them?
The amount of work that a car must do to slow down is proportional to the kinetic energy (KE) change.
The entity that the car is pushing against to slow it down is actually doing negative work, of the same magnitude.
The ratio of the KE changes is
[(20)^2 - (10)^2]/10^2
= 300/100 = 3
The deceleration from 20 to 10 kph requires that 3 times as much work be done by the car.
Note that I did not have to compute the KE or change speed units to m/s to get this result. Only the ratio is important for this problem.