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"#