Which Mass Travels Further When Stopped by the Same Force?

[astro_kat]

Forces velocity & position?!?

A 4.0 kg mass is moving with speed 2.0 m/s A 1.0 kg mass is moving with a speed of 4.0 m/s. Both objects encounter the same constant breaking force, and are brought to rest. Which object travels the greater distance before stopping?

A. the 1.0 kg mass
B. the 4.0 kg mass
C. Both travel the same distance
D. Cannot be determined

*answer is C, why?!?*

 

[cryptoguy]

ok you know the equation Vf^2 = Vi^2 +2AD. Rearrange it to solve for D

D = (Vf^2 - Vi^2)/(2A)
And A (acceleration) = F/M

So D = (Vf^2 - Vi^2)M/(2F)

Plug in the givens for Vi and M, (F is constant) and you'll get D = -8F for both

 

[Dick]

The kinetic energy is equal to the braking force times the distance travelled. They both have the same kinetic energy.