Question

If a particle starting from rest is moving with a uniform
acceleration of 10 ms -2, then the final velocity when it
covers a distance of 2 km is
​

Answer 1

Answer:

200m/sec is the right answer

Explanation:

u=0

a=10m/sec2

s=2km=2000m

2as=v*v-u*u

2*10*2000=v*v-0

40000=v*v

√40000=v

v=200m/sec

Answer 2

Answer :

Given:

Initial velocity = 0m/s

Acceleration = 10m/s^2

Distance = 2km

Convert the distance from kilometres to metres

because the S.I. unit of distance is meter .

Hence ,

1 kilometer = 1000 meters

2 kilometres = ? meters

=> 2 × 1000

=> 2000 meters.

Required to find:

1. Final velocity of the particle

Solution:

In the question is is given that a particle starting from rest moving with an acceleration of 10m/s^2

Since , the particle is at rest we can say that the initial velocity of the particle is 0m/s

With that acceleration it travelled 2 km ( 2000 meters ) and they asked us to find what is the final acceleration .

To solve this problem we need to know about the 3 equations of the motion.

In this 3 equations in motion 1 equation will help us to solve this question.

3 equations of motion

$1. \: \: v = u + at$

$2. \: \: s = ut + \frac{1}{2} a {t}^{2}$

$3. \: \: {v}^{2} - {u}^{2} = 2as$

This are the 3 laws of motion .

However , we are going to use the 3rd equation of motion to solve this question

Reasons is that most of the values are given

Let me explain what do the letters mean in the 3rd equation;

v = final velocity

u = initial velocity

a = acceleration

s = distance

So, let's solve this question using 3rd equation of motion.

Hence , Substitute the given values in that equation.

By substitution we get ;

$(v {)}^{2} - (0 {)}^{2} = 2 \times 10 \times 2000 \\ {v}^{2} - 0 = 40000 \\ {v}^{2} = 40000 \\ v = \sqrt{40000} \\ v = 200$

Therefore,

Final velocity of the particle is 200m/s .