# Thread: Particle Mechanics.

1. ## Particle Mechanics.

Take, the acceleration due to gravity 10 ms^-2.

A car of mass 500 kg has a maximum speed of 40 m/s on a level road with the engine of the car working at a constant power of 20 kW. The resistance to motion is proportional to the square of the speed.
a. Find the acceleration when the speed is 20 m/s.
b. Find the distance traveled with the speed increases from 20 m/s to 30 m/s.
c. When the car reaches the speed 30 m/s, the power is switched off. Find the time required to reduce the speed from 30 m/s to 20 m/s.

2. What ideas have you had so far?

3. Originally Posted by Ackbeet
What ideas have you had so far?
Thank you for your concern.

I'm stuck here.
I couldn't determine the resistance of motion (f_k).
As you can see there is statement saying in the question.
"The resistance of motion is proportional to the square of the speed"
So there must be a constant value as a multiplier factor of the speed so that the resistance proportional to the square of speed.
How can I find such a value?

4. You're going to have to use the phrase "proportional to the square of the speed" to write down an equation in order to get the force required to keep the car going at a constant speed that is different from 40 m/s. You've actually been able to correctly compute, thanks to the power information, the force required to keep the car in motion when the car is going 40 m/s. Honestly, I'm a little puzzled by the question, because if the speed is constant, and you're not changing direction, the acceleration of the car is zero! The kind of computation you're doing is probably what they're after. I would claim the question is a bit sloppy. Anyway. You need the equation $F = k v^{2}$. You know the force and the speed; that should enable you to compute k. Once you have k, you should be able to find the resistance force when the speed is 20 m/s. Make sense?