Question

A train starting from rest attains a velocity of 20 ms in 3 minutes .assumig that the acceleration in uniform find the accereleration (2)distance travelled by the train while it attained this velocity​

Answer 1

Given :

• initial velocity of train, u = 0

• final velocity of train, v = 20 m/s

• time taken by train to attain this velocity, t = 3 min = 3 × 60 sec = 180 sec

To find :

• acceleration of train, a = ?
• distance travelled by train while attaining final velocity, s = ?

Formulae required :

First equation of motion

• v = u + a t

Second equation of motion

• s = u t + 1/2 a t²

[ where v is final velocity, u is initial velocity , a is acceleration , t is time taken , s is distance covered ]

Solution :

Using first equation of motion

→ v = u + a t

→ 20 = (0) + a (180)

→ a = 20 / 180

→ a = 1/9  m/s²

therefore,

acceleration of the train is 1/9  m/s².

Now,

Using second equation of motion

→ s = u t + 1/2 a t²

→ s = (0) (180) + 1/2 × (1/9) (180)²

→ s = 1/2 × (1/9) × 32400

→ s = 1800 m

therefore,

distance travelled by train while attaining final velocity of 20 m/s is 1800 m.