Question

A train starts from rest and moves with a constant acceleration of $2.0m/s^2$ for half a minute. The brakes are then applied and the train comes to rest in one minute after applying breaks. Find (a) the total distance moves by the train, (b) the maximum speed attained by the train and (c) the position(s) of the train at half the maximum speed. (Assume retardation to be constant).

Answer 1

u=0 ( train starts from rest)

$a=2m/s^2$

$t=30second$

From (I) equation of motion

v = u+at

$v_0=60m/s$

(a)$s_1=\frac{1}{2}{v}_0\times \frac{1}{2}\times 60$=$\frac{1}{2}\times 60\times \frac{1}{2}\times 30=900m$

$s_2=\frac{1}{2}\times 60\times 60=1800m$

$s=2700m$

(b)$v_0=60m/s$

(c)$v^2=2as$

$(\frac{60}{2}{)}^2=2\times 2\times s$

$s=\frac{30\times 30}{2\times 2}=225m$