Answer

Verified

427.8k+ views

**Hint:**Newton’s second law of motion states that the force is equal to the rate of change of momentum. Force is equal to the mass times acceleration, for a constant mass. The given question is an application of Newton's second law of motion. In order to find the solution of the question write down the given physical quantities and apply the formula.

**Formula Used:**F = ma

**Complete answer:**

It is given in the question that,

Mass of the particle is, m = 5kg

Initial velocity, U = 0

Time, t = 2sec

We have to find the, Final speed of the particle, i.e. v =?

The relation between the potential energy and the conservative force is given as,

$\eqalign{

& \vec F = \dfrac{{du}}{{dx}}\hat i - \dfrac{{du}}{{dx}}\hat j - \dfrac{{du}}{{dx}}\hat k \cr

& \Rightarrow \vec F = \dfrac{{du}}{{dx}}\left( {7x + 24y} \right) - \dfrac{{du}}{{dx}}\left( {7x + 24y} \right) - 0 \cr

& \Rightarrow \vec F = \left[ { - 7\dfrac{d}{{dx}}\left( x \right) - 0} \right]\hat i - \left[ {7\left( 0 \right) + \dfrac{d}{{dy}}\left( {24y} \right)} \right]\hat j \cr

& \Rightarrow \vec F = - 7\hat i - 24\hat j \cr

& \Rightarrow F = \sqrt {{{\left( { - 7} \right)}^2} + {{\left( { - 24} \right)}^2}} \cr

& \therefore F = 25N \cr} $

We know that force is given by the formula,

F = ma

Where ‘F’ is the force, ‘m’ is the mass of the object or the particle and ‘a’ is the acceleration. Substituting acceleration ‘a’ as, $a = \dfrac{v}{t}$

we get, $F = m\left( {\dfrac{{v - u}}{t}} \right)$

Since the initial velocity ‘u’ of the particle is zero.

Substituting the value of force ‘F’ and mass ‘m’ of the particle we get,

$\eqalign{

& \Rightarrow 25 = 5\left( {\dfrac{{v - 0}}{2}} \right) \cr

& \therefore v = 10m{s^{ - 1}} \cr} $

Thus, the speed of particles at t = 2s is 10m/s.

**Hence, option (d) is the correct answer.**

**Note:**

A conservative is defined as the force for which the total work done to move a particle between two given points is independent of the path taken.

Students should remember that in case of conservative forces such as gravitational force, electrostatic force, force is taken as, F = $ - \dfrac{{dU}}{{dx}}$.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE