Question on Physics?

Question

A car braking system supplies a constant force. calculate the work required to change the speed from 30 m/s to 25 m/s. Calculate the work required to change the speed from 15 m/s to 0 m/s. Compare the distances of travel for each situation. (Hint: make a ratio of the first case to the second case)



In the first problem, if the car went from 30 m/s to 0 m/s, then what is the comparison now to 15 m/s to 0 m/s?



If you could please show the work too, it might help me understand it a little better and I can compare my work to see where I am messing up. thank you

Answer 1

Work is given as
W=Fd where
W - work done
F -force applied over a distance d parallel to the direction of force.
We also know that
F=ma

and (see ref. supplied)
a=(Vf^2 - Vi^2) / 2 d

then

W=Fd= m a d (no pun intended :-) )
W= m [(Vf^2 - Vi^2) / 2 d] d
W= m (Vf^2 - Vi^2) / 2
The only thing you need is the mass of the vechicle.

(a) W1=m(30^- 25^2)/2= 137.5 m Joules
(b) W2=m(15^2 - 0)/2= 112.5 m Joules

W1/W2=137.5 m/112.5 m = 1.22

(c)W1=m(30^- 0)/2= 450 m Joules
W2=m(15^2 - 0)/2= 112.5 m Joules

w1/w2= 450/112.5= 4

Let me know if you have any questions.