Question

What is the final velocity of a train that accelerates from 15 m/s for 12 s and has an acceleration of 0.75 m/s²?

A. 15 m/s
B. 22.5 m/s
C. 27 m/s
D. 30 m/s

Answer 1

Main Answer:

The final velocity of the train is 24 m/s. This is calculated using the kinematic equation: final velocity = initial velocity + (acceleration * time).

In the given scenario:

`\[ \text{Initial velocity} (u) = 15 \, \text{m/s} \]`

`\[ \text{Acceleration} (a) = 0.75 \, \text{m/s}^2 \]\[ \text{Time} (t) = 12 \, \text{s} \]`

Using the kinematic equation:

`\[ \text{Final velocity} (v) = u + (a \cdot t) \]`

`\[ v = 15 + (0.75 \cdot 12) = 24 \, \text{m/s} \]`

Step-by-step explanation:

The calculation involves simple substitution of the given values into the kinematic equation. The initial velocity of 15 m/s is added to the product of acceleration (0.75 m/s²) and time (12 s). This yields a final velocity of 24 m/s. The process reflects the basic principles of kinematics, where velocity is determined by the initial velocity, acceleration, and time. It's essential to accurately plug in the values and follow the equation to arrive at the correct final velocity.

In summary, the final velocity of the train, after accelerating from 15 m/s for 12 seconds with an acceleration of 0.75 m/s², is 24 m/s. This result is obtained by applying the kinematic equation, which relates initial velocity, acceleration, and time.

Therefore, the correct answer is A. 15 m/s.