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. ?

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Answer 1 · 2018-07-07T15:44:18

Refer to the explanation.

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

So here, the speed in $"m/s"$ is:

$50/3.6~~13.9 \ "m/s"$

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

$v=u+at$

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:

$t=(v-u)/a$

$=(13.9 \ "m/s"-0 \ "m/s")/(1.5 \ "m/s"^2)$

$~~9.27 \ "s"$

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

$d=v_"avg"*t$

where:

$d$ is the distance traveled

$v_"avg"$ is the average velocity of the train

$t$ is the time taken

Here, $v_"avg"=(13.9 \ "m/s")/2=6.95 \ "m/s"$ .

So, the distance traveled is then:

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

$~~64.4 \ "m"$