Question

A train is moving at an initial velocity of 9 meters/second. It has a constant acceleration of -3 meters/sec^2. It is at an initial position of 24 meters. Moments later, it is at a final position of 0 meters.

a) What is the final velocity of the train?
b) How long did it take for the train to come to a stop?
c) What is the acceleration of the train?
d) What is the displacement of the train during this time?

Answer 1

a) The final velocity of the train is 0 m/s. b) It takes 3 seconds for the train to come to a stop. c) The acceleration of the train is -3 m/s². d) The displacement of the train is 13.5 meters.

Step-by-step explanation:

a) To find the final velocity of the train, we can use the equation:

v_f = v_i + at

Where:

• v_f is the final velocity
• v_i is the initial velocity
• a is the acceleration
• t is the time

Plugging in the values, we get:

v_f = 9 + (-3)(t)

Since the train comes to a stop, its final velocity is 0. We can solve for t:

0 = 9 - 3t

t = 3 seconds

Therefore, the final velocity of the train is 0 m/s.

b) To find the time it takes for the train to come to a stop, we already found that t = 3 seconds.

c) The acceleration of the train is -3 m/s².

d) To find the displacement of the train, we can use the equation:

s = v_i * t + 0.5 * a * t²

Plugging in the values, we get:

s = 9 * 3 + 0.5 * (-3) * 3²

s = 27 - 13.5

s = 13.5 meters