Need help with simple mechanics problem

[issacnewton]

here's the problem.

a 1200kg vehicle is traveling at 20m/s along a level road. the force of friction opposing the vehicle's motion is 450 Newtons. the vehicle's motor is switched off and it continues to roll for 12 seconds...

we have to find the deceleration and the distance travelled... now i am getting two different answers for the deceleration

a= F/m = 450 / 1200 = 0.375 m/s^2

and a = (v-u)/t = 0-20/12 = -1.67 m/s^2

there is also another point about finding distance... since assuming that the vehicle is coming to rest, the work done by the friction must be equal to the kinetic energy of the vehicle at the instant when the motor is switched off.
so K = 1/2 m v^2 = 1/2 * 1200 * 20^2 = 240000 J

if the distance traveled is s then K = F * s
s = K/F = 240000/450 = 533.33 m

but this doesn't seem to be the right answer since this distance is more than the distance the vehicle would have traveled in 12 sec, in the absence of the friction force...

so what's happening here ?


please help

 

[NanakiXIII]

Does the problem actually state that the vehicle comes to a stop after those twelve seconds?

 

[thomate1]

Hello,

Thank you for reaching out for help with your mechanics problem. It seems like you have made some progress in finding the deceleration and distance traveled, but you are getting two different answers for the deceleration and the distance traveled seems to be too long. Let's take a closer look at the problem and see if we can figure out what's going on.

First, let's review the information we have been given. We know that the vehicle has a mass of 1200 kg and is traveling at a speed of 20 m/s. The force of friction opposing the vehicle's motion is 450 Newtons. The vehicle's motor is switched off, and it continues to roll for 12 seconds.

To find the deceleration, we can use the equation a = F/m, where F is the force of friction and m is the mass of the vehicle. When we plug in the values, we get a = 450 N / 1200 kg = 0.375 m/s^2. This is the correct value for the deceleration.

Next, let's look at the equation you used to find the distance traveled, s = K/F. This equation is correct, but we need to make sure we are using the correct value for K. The kinetic energy of the vehicle at the instant the motor is switched off is not equal to the total kinetic energy of the vehicle. Remember, the vehicle is still moving at a speed of 20 m/s when the motor is switched off, so the total kinetic energy would be 1/2 * 1200 kg * (20 m/s)^2 = 240,000 J. However, at the instant the motor is switched off, the vehicle only has a kinetic energy of 1/2 * 1200 kg * (20 m/s)^2 - 450 N * 12 s = 228,000 J. This is because the friction force is doing work on the vehicle, which is causing it to slow down. So, when we plug in this value for K, we get s = 228,000 J / 450 N = 506.67 m. This is the correct distance traveled.

It may seem counterintuitive that the distance traveled is longer than it would be without the friction force, but remember that the friction force is slowing down the vehicle, so it takes longer for the vehicle to come to a complete stop. I hope this helps clarify the