Question

A particle of mass m=0.1 kg is initially at rest at origin. It starts moving with a uniform acceleration a = 10 ms at t=o. The action s of the partice in units of J-S at t=2s is .

Answer 1

To calculate the action (work) done by the particle after 2 seconds, we use the formula Action (s) = (1/2) * mass * velocity^2, where velocity is the final velocity after 2 seconds. We can find the final velocity by using the formula final velocity = initial velocity + (acceleration * time). Substituting the values into the formulas, we can calculate the action (s) of the particle after 2 seconds.

Step-by-step explanation:

In this problem, we are given the mass of a particle, its initial velocity (which is zero), and its uniform acceleration. We are asked to find the action (work) done by the particle after 2 seconds.

The action (work) done by a particle is given by the formula: Action (s) = (1/2) * mass * velocity^2.

Since the particle starts from rest, its initial velocity is zero. Using the given acceleration, we can calculate the particle's final velocity after 2 seconds using the formula: final velocity = initial velocity + (acceleration * time).

Substituting the values into the formula, we can find the final velocity. Then, substituting the mass and final velocity into the formula for action, we can calculate the action (s) of the particle after 2 seconds.

Answer 2

40 J-s

Step-by-step explanation:

Given:

mass of the particle, m=0.1 kg

Acceleration of the particle, a = 10 m/s²

Time interval, ΔT = 2 - 0 = 2 seconds

Since the particle is initially at rest,

therefore the initial speed u = 0 m/s

The action, s is calculated as :

s = Force × distance × time interval

now,

from the Newton's equation of motion, we have

`S = ut+(1)/(2)at^2`

where, S is the distance traveled after 2 seconds

on substituting the values, we have

`S = 0*2+(1)/(2)*10*2^2`

or

S = 20 m

also,

Force = mass × acceleration

thus,

Force = 0.1 × 10 = 1 N

on substituting the values, in the formula for the action, we get

s = 1 × 20 × 2

or

s = 40 J-s