A train starts from rest and moves with a constant acceleration of $2.0 m s^{- 2}$ for a half minute. The brakes are then applied and the train domes to rest in one minute. Find the position(s) of the train at half the maximum speed.

225 m

and

2.50 k m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

125 m

and

1.75 k m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

175 m

and

2.25 k m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

225 m

and

2.25 k m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C $225 m$ and $2.25 k m$
Velocity of train at the end of half minute= $v_{m a x} = u + a t = 2 m / s^{2} \times 30 s$
Distance traveled by train to attain $v = 15 m / s$ is
$s_{1} = \frac{v^{2}}{2 a} = 225 m$
After half a minute, train comes to rest in one minute.
Hence $v = a_{b r a k e} t_{b r a k e}$
$a_{b r a k e} = \frac{v}{t_{b r a k e}} = 1 m / s^{2}$
Hence distance further traveled to attain speed $15 m / s$ is
$s_{2} = \frac{v_{m a x}^{2} - v^{2}}{2 a_{b r a k e}}$
$= 337.5 m$
Distance traveled to attain $v_{m a x} = s_{3} = \frac{1}{2} a t^{2} = 900 m$
Hence position of train = $s_{2} + s_{3} = 1.237 k m$

Suggest Corrections

Similar questions

Q. A train starts from rest and moves with a constant acceleration of

2.0 m / 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).

A train starts from rest and moves with a constant acceleration of 2.0 $\frac{m}{s^{2}}$ fbr half a minute. The brakes are then applied and the train comes to rest in one minute. Find.

(a) the total distance moved. by the train,

(b) the maximum speed attained by the train and

Q. A train starts from rest and accelerates uniformly at a rate of

2 m s^{- 2}

for

10 s

. It then maintains a constant speed for

200 s

. The brakes are then applied and the train is uniformly retarded and comes to rest in

50 s

. Find the average velocity of the train.

Join BYJU'S Learning Program

A train starts from rest and moves with a constant acceleration of 2.0ms−2 for a half minute. The brakes are then applied and the train domes to rest in one minute. Find the position(s) of the train at half the maximum speed.

A train starts from rest and moves with a constant acceleration of $2.0 m s^{- 2}$ for a half minute. The brakes are then applied and the train domes to rest in one minute. Find the position(s) of the train at half the maximum speed.