physics questions???

Question

alright i just took a test and am wicked confused on these 2 problems, any insight of what vormula or anything i should have used.. thanks...
A) a 1000kg car J of work are done on a 1110 kg car while it accelerates from 10 m/s to some final velocity. find this velocity?


thanks in advance!!!

for some reason i typed the questions and it messed up.... ill re-type it here!!
A) 1000kg car experiences a net force of 9500 N while decelerating from 30m/s to 23.4m/s. how far does it travel while slowing down?

B) 4.00x10^5 J of work are done on a 1110kg car while it accelerates from 10 m/s to some final velocity. what is that final velocity?

Answer 1

A) Find the acceleration of the car = F/m = 9500/1000 = 9.5 m/sec^2. The change in velocity is ∆V = a*∆t, so you can find how long it took to change velocity: ∆t = ∆V/a = (30-23.4)/9.5=0.695 s

An object under constant acceleration a will travel a distance s =0.5*a*t^2 in time t. So the distance traveled is

0.5*9.5*(0.695^2) = 2.29 m

B) Find the final velocity by equating the work done to the change in energy: The initial energy is 0.5*1110*10^2 = 55,500 J. To this you added 400,000 J so the final energy is 455,500 J. This must equal 0.5*m*v^2, where v is the final velocity, so

0.5*1110*v^2 = 455,500

v^2 = 455,500/555 = 820.7

v = 28.65 m/sec

Answer 2

A)

By equation: F = m a
9500 = 1000 a
a = 9.5 m/s2

By equation: v^2 - u^2 = 2 a s
(23.4)^2 - (30)^2 = 2 (-9.5) s
s = 18.5 metre

Note:

In this case, you cannot find the distance by s = 0.5 a t^2 because the velocity at the begining is not zero. The correct equation is s = u t + 0.5 a t^2.

By equation: s = u t + 0.5 a t^2
s = (30) (0.695) + 0.5 (-9.5) (0.695)^2
s = 18.5 metre

the correct answer should be 18.5 metre.

Moreover, the force acting on the car makes it decelerates. So the acceleration of the car is negative, not 9.5 m/s2

B)

By equation: KE = (m/2) (v^2 - u^2)
(4.00 x 10^5) = (1110/2) (v^2 - 10^2)
u = 28.6 metre per second

Answer 3

A)
Force*distance = change in K.E
F*d = 0.5 m [v^2 - u^2]
d = 0.5 m [v^2 - u^2] /F
d = 0.5*1000* [30^2 - 23.4^2] / 9500
d= 18.55 m
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B)
Change in K.E = Work
0.5 m [V^2 - U^2] = 400000 J.
V^2 - U^2 = [800000 / 1110] =720.720
V^2 = 720.720 + 10^2 =820.720
V = 28.65 m/s.
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