Question

a 75 m long train begins uniform acceleration from rest. the front of the train passes a railway worker 140m down the track at speed of 25m/s what will be the speed of the last car as it passes the worker?

Answer 1

$\huge{\text{\underline{Solution:-}}}$

★ Given:-

Train length = 75m

Initial velocity = 0

A worker is 180 m from the front of the train.

The front passes the worker going at 23 m/s.

The rear end is 75 + 180m from the worker = 255 m

$\huge{\text{\underline{Explaination:-}}}$

To find the acceleration:-

Now, using V = u + at

But u = 0

Doing the substitution we have :

23 = at

a = 23 / t

★ By using S = u + 0.5at²

Again u = 0

180 m = 0.5at²

a = 180/0.5t²

a = 360/t²

360/t² = 23/t

360t = 23t²

Divide through by 23t we have :

360t / 23t = t

t = 15.65 seconds.

a = 23 / 15.65

$\tt{\boxed{a = 1.4696 m/s^2}}$

Now we can calculate velocity of last car.

S = 0.5at² (since u =0)

255 = 0.5 × 1.4696 × t²

t² = 255/ 0.7348

t² = 347.03

t = √347.03

$\tt{\boxed{t = 18.63 seconds}}$

$\tt{\boxed{V = at}}$

= 18.63 × 1.4696 = 27.38 m/s

$\tt{\boxed{= 27.38 m/s}}$