In order to increase the kinetic energy of a speeding train by 44%, 42MJ of work must be performed (1 MJ = 106 J). If the final velocity of the train (after the 42 MJ of work) is 9 m/s, what is the mass of the train in metric tons (1 metric ton = 1000 kg)?

Explanation:

100 % increase makes an amount 2 times .

44 % increase = 42 MJ

100 % increase = 95.45 MJ

final kinetic energy = 2 x 95.45 MJ

= 190.9 x 10⁶ J

1/2 m v² = 190.9 x 10⁶

.5 x m x 9² = 190.9 x 10⁶

m = 4.71 x 10⁶ kg

= 4710 metric ton .

d) physical means can be used to separate the components of air.

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s