Question

In the 1950s, an experimental train, which had a mass of 2.50X10^4 kg, was powered across a level track by a jet engine that produced a thrust of 5.00X10^5 N for a distance of 509m.
a. Find the work done on the train
b. Find the change in Kinetic energy.
c. Find the final kinetic energy of the train if it started from rest.
d. Find the final speed of the train if there had been no fricion.

Answer 1

What is the formula for work?

Answer 2

Its \[W=F \Delta x\] I belive.

Answer 3

Yes,
Work = (Force) x (Distance over which force is applied)

Given that, what is the answer to (a) ?

Answer 4

Im not sure if I did it right, but I got 127,250,000.

Answer 5

We have force, F = 5.00X10^5 N and
displacement over which the force is applied, d = 509m.

Calculate

Work = F d

Answer 6

Okay, then it would be 254,500,000?

Answer 7

Yes, but better to put it in scientific notation:

W = 2.545 x 10^8 J

Answer 8

Now, by the Work-Energy theorem,
Change of energy = Work.

That being the case, what is the change in Kinetic Energy?

Answer 9

2.545x10^8 J?

Answer 10

Yes, exactly. hence the answer to (c) is ...

Answer 11

The same?

Answer 12

yes. By definition,
(change in KE) = KE(end) - KE(beginning).

If KE(beginning) = 0, it must be that
KE(end) = (change in KE)

Answer 13

Now, how do you answer (d)?

Answer 14

Use the formula for Kinetic Energy and equal it to the work?

Answer 15

You know already the value of KE(end). Set that equal to the formula for Kinetic Energy, which is what ?

Answer 16

254,500,000 or 2.545 x 10^8 J?

Answer 17

Right, that's the value of KE(end). Now, as a function of mass and speed, what is the formula for Kinetic Energy?

Answer 18

\[ KE = \frac{1}{2} mv^2 \]
where m is the mass of the object and v its speed.

Now use this to solve for v.