Question

a body of mass 5 kg changes it's velocity from 2 to5 in 4 seconds . calculate the rate of change to work done and force acting on the object​

Answer 1

Answer:

f= m× a

5×5_2/4

5×3/4

15/4N

Answer 2

Given :

• Mass of the body = 5 kg.

• Initial velocity = 2 m/s.

• Final Velocity = 5 m/s.

• Time Taken = 4 s.

To find :

• Work done

• Force exerted

Solution :

First let us find the Acceleration of the body.

We know the Third Equation of Motion ,i.e,

$\boxed{\bf{v = u + at}}$

Where :

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

$:\implies \bf{5 = 2 + a \times 4}$

$:\implies \bf{5 - 2 = a \times 4}$

$:\implies \bf{3 = a \times 4}$

$:\implies \bf{\dfrac{3}{4} = a}$

$:\implies \bf{0.75 = a}$

$\boxed{\therefore \bf{a = 0.75\:ms^{-2}}}$

Hence the acceleration of the body is 0.75 m/s².

Now let us find the distance covered by the body :

We know the Third Equation of Motion ,i.e,

$\boxed{\bf{v^{2} = u^{2} + 2aS}}$

Where :

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• S = Distance

Now using the third equation of motion and substituting the values in it, we get :

$:\implies \bf{v^{2} = u^{2} + 2aS}$

$:\implies \bf{5^{2} = 2^{2} + 2 \times 0.75 \times S}$

$:\implies \bf{5^{2} = 2^{2} + 1.5S}$

$:\implies \bf{25 - 4 = 0.75}$

$:\implies \bf{21 = 0.75 S}$

$:\implies \bf{21 = \dfrac{75}{100}S}$

$:\implies \bf{21 \times \dfrac{100}{75} = S}$

$:\implies \bf{7 \times \dfrac{100}{25} = S}$

$:\implies \bf{7 \times 4 = S}$

$:\implies \bf{28 = S}$

$\boxed{\therefore \bf{S = 28\:m}}$

Hence the distance covered by the body is 28 m.

To find the force exerted on the body :

We know the formula for force i.e,

$\boxed{\bf{F = ma}}$

Where :

• F = Force
• m = Mass
• a = Acceleration

Now by substituting it in the equation , we get :

$:\implies \bf{F = ma}$

$:\implies \bf{F = 5 \times 0.75}$

$:\implies \bf{F = 3.75}$

$\boxed{\therefore \bf{F = 3.75\:N}}$

Hence the force exerted by the body is 3.75 N.

Work done by the body :

We know the formula for Work Done i.e,

$\boxed{\bf{W = Fs}}$

Where :

• W = Work Done
• F = Force
• S = Displacement

Now by substituting it in the equation , we get :

$:\implies \bf{W = Fs}$

$:\implies \bf{W = 3.75 \times 28}$

$:\implies \bf{W = 105}$

$\boxed{\therefore \bf{W = 105\:J}}$

Hence the work done by the body is 105 J.