A roller-coaster train at rest has a mass of 30 tons If force 50000 N acts on it for 12 s then what is its momentum after that time and velocity?

- Mass of the roller-coaster train, $m = 30$ tons

- Force acting on the train, $F = 50000$ N

- Time for which the force acts, $t = 12$ s

To find:

- Momentum of the train after 12 s, $p$

- Velocity of the train after 12 s, $v$

Solution:

1. Momentum after 12 s, $p$

Momentum is defined as the product of mass and velocity. Since the train starts from rest, its initial velocity is zero. Therefore, the momentum of the train after 12 s is:

$$p = mv$$

$$=(30 \text{ tons})(9.81 \text{ m/s}^2)(12 \text{ s})$$

$$=353040 \text{ kg m/s}$$

2. Velocity of the train after 12 s, $v$

We can find the velocity of the train after 12 s using the equation of motion:

$$v = u + at$$

where,

- $u$ is the initial velocity (in this case, $u = 0$)

- $a$ is the acceleration

- $t$ is the time

We can find the acceleration using Newton's second law:

$$F = ma$$

$$a = \frac{F}{m}$$

$$=\frac{50000 \text{ N}}{30000 \text{ kg}}$$

$$=1.67 \text{ m/s}^2$$

Substituting the values of $u$, $a$, and $t$ in the equation of motion, we get:

$$v = 0 + (1.67 \text{ m/s}^2)(12 \text{ s})$$

$$=20.04 \text{ m/s}$$

Therefore, the momentum of the roller-coaster train after 12 s is 353040 kg m/s and its velocity is 20.04 m/s.