Question

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. ?

Answer 1

Refer to the explanation.

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"`