Question

The velocity of a particle of mass 250 g changes from 10 m/s

to 16 m/s in 3 seconds. Assuming that a constant force acts on it,

find the magnitude of the force.​

Answer 1

Answer:

Mass = 250 g or, 0.25 kg

Initial Velocity (u) = 10 m/s

Final Velocity (v) = 16 m/s

Time (t) = 3 s

Acceleration = (v-u)/t

= (16-10)/3 ms⁻²

= 6/3 ms⁻²

= 2 ms⁻²

Force = Mass*Acceleration

= 0.25*2 N

= 0.5 N

Hope this helps.

Answer 2

Given :

• Mass of the particle = 250 g

• Initial velocity = 10 m/s

• Final Velocity = 16 m/s

• Time taken = 3 s

To find :

The magnitude of the force.

Solution :

To find the force , first we have to find accelaration produced by the Particle.

To find the Acceleration produced by the particle :

Using the First Equation of Motion and substituting the values in it, we get :

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

Where :-

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

$:\implies \bf{16 = 10 + a \times 3}$

$:\implies \bf{16 - 10 = a \times 3}$

$:\implies \bf{16 - 10 = 3a}$

$:\implies \bf{6 = 3a}$

$:\implies \bf{\dfrac{6}{3} = a}$

$:\implies \bf{\dfrac{\not{6}}{\not{3}} = a}$

$:\implies \bf{2 = a}$

$\boxed{\therefore \bf{Acceleration\:(a) = 2\:ms^{-2}}}$

Hence the acceleration produced is 2 m/s².

Magnitude of Force :

We know that :-

• Acceleration = 2 m/s²

• Mass = 250 g

First ket us convert the mass in it's SI unit i.e, kg from g.

We know that ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀1 kg = 1000 g

Hence ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀==> 250 g = 250/1000

⠀⠀⠀⠀⠀⠀⠀⠀⠀==> 250 g = 0.25 kg

Using the formula for force exerted and substituting the values in it, we get :-.

$\boxed{:\implies \bf{Force\:(F) = Mass\:(M) \times Acceleration\:(a)}}$

$:\implies \bf{F = 0.25 \times 2}$

$:\implies \bf{F = 0.5}$

$\boxed{\therefore \bf{Force\:(F) = 0.5\:N}}$

Hence the magnitude of force is 0.5 N.