# C) If a train accelerates at 1.5 m/s2 calculate the time taken to increase its velocity from rest to 50 km/h and the distance travelled in this time. ?

Jul 7, 2018

Refer to the explanation.

#### Explanation:

We first convert to $50 \setminus \text{km/h}$ to $\text{m/s}$. Note that $1 \setminus \text{m/s"=3.6 \ "km/h}$.

So here, the speed in $\text{m/s}$ is:

$\frac{50}{3.6} \approx 13.9 \setminus \text{m/s}$

Then to find the time taken, we use the equation:

$v = u + a t$

where:

• $v$ is the final velocity of the train

• $u$ is the initial velocity of the train

• $a$ is the train's acceleration

• $t$ is the time taken

So, we get:

$t = \frac{v - u}{a}$

$= \left(13.9 \setminus {\text{m/s"-0 \ "m/s")/(1.5 \ "m/s}}^{2}\right)$

$\approx 9.27 \setminus \text{s}$

To find the total distance traveled, we use the equation:

$d = {v}_{\text{avg}} \cdot t$

where:

• $d$ is the distance traveled

• ${v}_{\text{avg}}$ is the average velocity of the train

• $t$ is the time taken

Here, ${v}_{\text{avg"=(13.9 \ "m/s")/2=6.95 \ "m/s}}$.

So, the distance traveled is then:

d=(6.95 \ "m")/(color(red)cancelcolor(black)"s")*9.27color(red)cancelcolor(black)"s"

$\approx 64.4 \setminus \text{m}$