Question

A train starts from a station at point A and accelerates uniformly to a speed of 20m/s. It maintains this speed and then retards uniformly until it comes to rest at point B. The distance between the stations is 2000m the total time taken is 2 minutes.if the acceleration is twice the retardation. a) draw a velocity time graph. b) find the time for which the train is moving at constant speed. c) find it's retardation

Answer 1

Solution.

$v_0=0 m/s;$

$v=20 m/s;$

$a=2a_1;$

$t=120s;$

$a)$

$b)\dfrac{v^2}{2a}+\dfrac{v^2}{2a_1}+v\tau=2000;$

$\dfrac{v}{2a}+\dfrac{v}{a_1}+\tau=120;$

$3v^2+4a_1v\tau=8000a_1;$

$3v+2a_1\tau=240a_1;$

$1200+80a_1\tau=8000a_1;$

$60+2a_1\tau=240a_1;$ |$\sdot40$

$1200+80a_1\tau=8000a_1;$

$2400+80a_1\tau=9600a_1;$

$-1200=-1600a_1;$

$a_1=0.75 m/s^2;$

$2a_1\tau=240a_1-3v;$

$\tau=\dfrac{240\sdot0.75-60}{2\sdot0.75}=80s;$

$c)a_1=0.75 m/s^2;$

Answer: $b)\tau=80s;$

$c)0.75 m/s^2.$