Question

19.
A train moves with a velocity of 10m/s. Then driver decided to accelerate and applies a
constant acceleration of 2m/s. Find the velocity of the train after covering 100m.
A) 10 m/s
B) 10 5 m/s
C) 5m/s
D) 20m/s
E) V10 m/sm​

Answer 1

Question:

• A train moves with a velocity of 10m/s. Then driver decided to accelerate and applies a constant acceleration of 2m/s. Find the velocity of the train after covering 100m.

Given:

• initial velocity = 10 m / s
• acceleration = 2 m / s ²
• Total distance covered= 100 m

To find :

• final velocity

Solution :

As per the 3 rd kinematic equation,

$\boxed{{v}^{2} = {u}^{2} + 2as}$

here ,

• v = final velocity
• u = initial velocity
• a = acceleration
• s = distance

Now substituting the given values in the above equation we get ,

$\implies{{v}^{2} = 100 + 2 \times 2 \times 100}$

$\implies{{v}^{2} = 500}$

$\boxed{v = 10 \sqrt{5} \frac{m}{s} }$

Answer 2

Given ,

Initial velocity (u) = 10 m/s

Acceleration (a) = 2 m/s²

Displacement (s) = 100 m

We know that , the Newton's third equation of motion is given by

(v)² - (u)² = 2as

Thus ,

(v)² - (10)² = 2 × 2 × 100

(v)² - 100 = 400

(v)² = 500

v = √500

v = 10√5 m/s

$\sf \therefore \underline{The \: final \: velocity \: of \: train \: is \: 10 \sqrt{5} \: m/s}$