Answer to Question #88496 in Mechanics | Relativity for Diamontay Thames

Question

A train traveling at 7.55 m/s accelerates to a distance of 975 m in 31.5 s. What is the final velocity of the train?

Answer 1

We can find the final velocity of the train from the kinematic equation:

$$d = \dfrac{v_i + v_f}{2} \cdot t,$$

here, $v_i = 7.55 m/s$ is the initial velocity of the train, $v_f$ is the final velocity of the train, $d = 975 m$ is the distance traveled by the train, $t = 31.5 s$ is the time during which the train accelerates.

Then, from this formula we can find the final velocity of the train:

$$v_f = \dfrac{2d}{t} - v_i = \dfrac{2 \cdot 975 m}{31.5 s} - 7.55 \dfrac{m}{s} = 54.35 \dfrac{m}{s}.$$

Answer:

$v_f = 54.35 \dfrac{m}{s}.$