Question

a train starting from rest attains a velocity of 72 km per hour in 5 minutes as using that the acceleration is uniform find out the acceleration the distance travelled by the train for attending this velocity​

Answer 1

Given :

Initial velocity (u) = 0 m/s

(Because the train is staring from rest)

Final velocity (v) = 72 km/hr

Time (t) = 5 min

Find :

The acceleration (a) and distance (s) travelled by the train.

Solution :

We know that

v = u + at

(From 1st eqof Motion)

Before putting the values in above formula. First we have to convert k/hr into m/s and min into sec.

To convert km/hr into m/s multiply with 5/18 and to convert min into sec multiply with 60.

• v = 72 km/hr = 72 × 5/18 = 20 m/s
• u = 0 km/hr = 0 × 5/18 = 0 m/s
• t = 5 min = 5 × 60 = 300 sec

Now, put the values in formula

=> 20 = 0 + a(300)

=> 20 = 300a

=> a = 0.067 m/s²

∴ Acceleration is 0.067 m/s²

Now,

s = ut + 1/2at²

(From 2nd equation of motion)

We have ..

• u = 0 m/s
• t = 300 min
• a= 0.067 m/s²

Substitute the known values in above formula

=> s = 0(300) + 1/2 × (0.067)(300)²

=> s = 0 + 1/2 × 0.07 × 90000

=> s = 6000/2

=> s = 3000 m

=> s = 3 km

∴ Distance travelled by train is 3 km.

Answer 2

SOLUTION:-

Given:

⚫A train starts from rest attains a velocity of 72km/hr. in 5 minutes.

⚫Time of travel= 5minute

We convert in second

1 minutes= 60 second

So,5 Minutes= 5× 60= 300seconds

⚫Initial velocity= 0

Therefore,

Velocity attained by the train:

$v = 72 \frac{km}{h} \\ \\ = > \frac{72 \times 1000}{60 \times 60} \\ \\ = > 20m / s$

Now,

CASE 1:

Using first equation of motion:

ACCELERATION

$a = \frac{v - u}{t} \\ \\ = > a = \frac{20 - 0}{300} \\ \\ = > a = \frac{20}{300} \\ \\ = > a = \frac{1}{15} m / s$

CASE 2:

Using second equation of motion:

DISTANCE TRAVELLED

$s = ut + \frac{1}{2} at {}^{2} \\ \\ = > s = 0 \times 300 + \frac{1}{2} \times \frac{1}{15} \times (300) {}^{2} \\ \\ = > s = 0 \times 300 + \frac{1}{30} \times 300 \times 300 \\ \\ = > s = 0 + \frac{90000}{ 30} \\ \\ = > s = 3000m$

Hence,

Distance travelled by train is 3km.

Hope it helps ☺️