Question

. A train starts from rest. It moves through 1 Km in 100 s with uniform acceleration.
What will be its speed at the end of 100 s.

Answer 1

Given :

• Initial velocity, u = 0 m/s (as it is starts from rest)

• Distance, s = 1 km = 1000 m

• Time, t = 100 seconds

To find :

• Speed, v

According to the question,

➞ s = ut + ½ at²

Where,

• s = Distance
• a = Acceleration
• t = Time
• u = Initial velocity

➞ 1000 = 0 × ½ 100 + a × 100 × 100

➞ 1000 = 0 + 5000a

➞ 1000 - 0 = 5000a

➞ 1000 = 5000a

➞ 1000 ÷ 5000 = a

➞ 0.2 = a

So,the acceleration is 0.2 m/s².

Now,

➞ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

➞ v = 0 + 0.2 × 100

➞ v = 0 + 20

➞ v = 20

So,the speed is 20 m/s.

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

═══════════════════

Answer 2

Answer :-

• Final velocity (v) = $\boxed{\textsf{\textbf{\red{ 20\:m/s}}}}$

Given :-

• Initial velocity (u) = 0 m/s

• Distance travelled (S) = 1 km

• Time taken (t) = 100 s

To find :-

• Final velocity of train.

Formula used :-

• $\boxed{\sf{S = \left(\dfrac{u+v}{2}\right)t}}$

Solution :-

$\sf{➪\:S = \left(\dfrac{u+v}{2}\right)t}$

$\sf{➪\:1000 = \left(\dfrac{0+v}{2}\right)(100)}$

$\sf{➪\:v = \dfrac{10\cancel{0}\cancel{0}}{1\cancel{0}\cancel{0}}\times 2}$

$\sf{➪\:}$$\textsf{\textbf{v = 20\:m/s}}$