Question how to solve car problem

[jaye21]

Hi all, I am not sure if this is the right place to post this as I am new to the boards. So sorry if it is not.

I received a bunch of HW assignments for the weekend and I'm just not understanding some of the concepts. I was wondering if anyone could help start me off on a couple problem. Any help would be appreciated thanks!


The position of a 2kg particle moving in the x-y plane varies as a function of time according to the expression r = [ (6t+1)m]i + [ (-5t^2 + 8t +3)m ]j

- find the work done between t=1 and t=5. Determine the power delivered to the particle at t=3.

? now I know how to do this problem given a function in relation to force. but not as a function of time. given as a function of time do i just subtract r(5) from r(1), or do I still have to integrate?

? with the power i am just very confused.



A 1000 kg car racing up an 80 m-high mountain road runs out of gas at a height of 45 m while traveling at 25 m/s. Cleverly, the driver shifts into neutral and coasts onward. ( Neglect friction and use conservation of mechanincal energy).

? will he clear the 80 m peak, show work. not having brakes at what speed will he reach the bottom.

No idea where to start on this one. If anyone could teach me it is just homework and I want to kno how to do this before next class. Thank you!

 

[arildno]

1. How are forces that act on an object related to the acceleration of the object and how is the acceleration of the object related to the position of the object?
These are the first 2 questions you should try to answer.

 

[M98Ranger]

Hi there, welcome to the boards! This is a great place to post your question and get some help.

For the first problem, you're on the right track - to find the work done, you would need to integrate the force function over the given time period. So in this case, you would integrate the force function (which can be found using the equation F = m(r''), where m is the mass and r'' is the second derivative of the position function) from t = 1 to t = 5. This will give you the total work done on the particle during that time period.

As for the power, it is defined as the rate of work done, so you would need to take the derivative of the work function with respect to time. Then, at t = 3, you can plug in the value and find the power delivered to the particle at that specific time.

For the second problem, you can use the conservation of mechanical energy to solve it. This means that the initial mechanical energy (kinetic energy + potential energy) will be equal to the final mechanical energy. So at the top of the mountain, the car's energy will be all potential energy. As it coasts down, it will convert that potential energy into kinetic energy. So you can set up an equation like this:

Initial potential energy = Final kinetic energy

mgh = (1/2)mv^2

Where m is the mass of the car, g is the acceleration due to gravity, h is the height, and v is the velocity. You can then solve for v and see if it is greater than or less than the initial velocity of 25 m/s. If it is greater, then the car will clear the peak. If it is less, then it will not clear the peak and will come to a stop at the bottom.

I hope this helps and good luck with your assignments! Remember to always show your work and ask for help if you need it.