Question

and answer the questions below.
A particle is moving with uniform acceleration Its velocity after 5 sec 25 ms-1 and after & 8 sec is 34 ms-1
Acceleration of the particle is

a)3/2ms -2
b) 3 ms-2
c) 6 ms-2
d) 9ms-2​

Answer 1

Answer:

option b) 3 m/s²

Explanation:

Given :

• A particle is moving with uniform acceleration.

• Its velocity after 5 sec is 25 m/s and after 8 sec is 34 m/s

To find :

the acceleration of the particle

Solution :

 Let the initial velocity be 'u'

Using first equation of motion,

v = u + at

where

v denotes final velocity

u denotes initial velocity

a denotes the acceleration

t denotes the time taken

After 5 sec,

v = u + a(5)

25 = u + 5a ➙ [1]

After 8 sec,

v = u + a(8)

34 = u + 8a ➙ [2]

Subtract equation [2] from equation [1],

34 - 25 = u + 8a - (u + 5a)

9 = u + 8a - u - 5a

9 = 3a

a = 9/3

a = 3 m/s²

∴ The acceleration of the particle is 3 m/s²

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Correct \: Question:- }}}$

A particle is moving with uniform acceleration. Its velocity after 5 second is 25m/s and after 8 sec is 34m/s. What is  the acceleration of the particle ?

$\large\underline{ \underline{ \sf \maltese{ \:Given:- }}}$

• A particle is moving with uniform acceleration.
• Its velocity after 5 sec is 25 m/s and after 8 sec is 34 m/s.

$\large\underline{ \underline{ \sf \maltese{ \:To\:Find:- }}}$

• Acceleration of the particle.

$\large\underline{ \underline{ \sf \maltese{ \:Solution:- }}}$

We know that, $\sf{\green{a={\dfrac{v-u}{t}}}}$

Let the initial velocity of the particle be-"u" m/s

So, for the first situation,

When t = 5second

$\sf{a=}{\dfrac{v-u}{t}}$

$\sf{\red{a={\dfrac{25-u}{5}}{\dots\dots\dots[1]}}}$

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For the 2nd situation,

When t =8second

$\sf{a=}{\dfrac{v-u}{t}}$

$\sf{\red{a={\dfrac{34-u}{8}}{\dots\dots\dots[2]}}}$

_________________________

From equation [1] and [2],

$\sf{{\dfrac{25-u}{5}}={\dfrac{34-u}{8}}}$

$\sf{\implies}{200-8u=170-5u}$

$\sf{\implies}{3u=30}$

$\sf{\green{\implies{u=10ms^{-1}}}}$

_________________________

Putting the value of u in [1]

$\sf{\implies}{a=}{\dfrac{25-u}{5}}$

$\sf{\implies}{a=}{\dfrac{25-10}{5}}$

$\sf{\implies}{a=}{\dfrac{15}{5}}$

$\sf{\implies}{\red{a=3\:ms^{-2}}}$

Therefore, the acceleration of the particle is 3m/s²

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