Physics Kinematics Problem

[albert611]

Hi, I attempted this problem, but I do not see how it makes sense. Could somebody give me an idea of how to solve this problem? Thanks!

While traveling along at 24.3 m/s, a 13.7 kg car runs out of gas 16 km from a service station. Neglecting friction, if the station is on a level 14.8 m above the elevation of the car, how fast will the car be going when it rolls into the station?

The correct answer should be 17.33 m/s BTW.

Thank you very much for your help!

-Albert

[Zlex]

Well, lets see.

Find the component of gravity that is slowing down the car. That'll be your negative acceleration. You have all the other information. Use the appropriate kinematic equation, plug and chug.

[aviv87]

Also, if you know how to calculate potential gravitational energy and kinetic energy you could use the energy conservation law.

[HallsofIvy]

In other words:
1) find the kinetic energy of the car using Ek= (1/2)mv2.
2) find the increase in potential energy as the car moves up to the gas station using
Ep= mgh.
3) find the kinetic energy of the car at the gas station assuming conservation of energy
4) find the speed of the car from the kinetic energy using, again Ek= (1/2)mv2.

[Tom McCurdy]

I would advise setting up the problem as follows
KE_i+U+i=KE_f+U_f
KE=Kinetic Energy
U=Potential Energy
KE=1/2 m v^2
U=mgy

We can assume the U_f will go to zero

1/2mv^2 = 1/2mx^2 + mgy solving for x

the m's cancel out

1/2 v^2 = 1/2 x^2 + gh

solve for x and volla 17.3323


so end the end you did not need to know the cars mass or the 16 miles... go conservation of energy

[tony873004]

A 13.7 kg car? It'll be blown away by the wind before it gets there!