Question

A body of mass 0.5 kg is resting on a frictionless surface.
When a force of 2000 dyne acts on it for 10 s, then calculate the distance traveled by it in 10 seconds.

Answer 1

Required answer :-

Distance travelled by the body in 10 seconds is 2 m

EXPLANATION :-

As per the given information we have,

• Mass of the body is (m) 0.5 kg
• The body is resting of frictionless surface [u =0]
• Force acting is 2000 dynes
• Time taken is 10 s

We have to find the distance travelled

From equations of motion,

We know that ,

$\implies \: s = ut + \dfrac{1}{2} at {}^{2}$

where,

• s = distance covered
• u = initial velocity
• t = time taken
• a = acceleration

So, we can apply this formula But we don't know the acceleration of the body . So,Lets calculate acceleration of body.

We know that,

$\implies \: f = ma$

• F = force
• m = mass
• a = acceleration

F = 2000 dynes

Converting dynes - Newtons

$\implies{F = 2000\times 10^{-5} N }$

$\implies{F = 2 \times 10^3× 10^{-5} N}$

$\implies{F = 2× 10^{-2}N}$

F = m × a

$\implies 2 \times 10 {}^{ - 2} = 0.5 \times a$

$\implies \dfrac{2}{100} = \dfrac{5}{10} \times a$

$\implies \dfrac{2}{10} = 5a$

$\implies \dfrac{1}{5} = 5a$

$\implies 25a = 1$

$\implies a = \dfrac{1}{25} \: m/s {}^{2}$

Substituting these values in formula

$\implies \: s = ut + \dfrac{1}{2} at {}^{2}$

$\implies \: s = 0(10) + \dfrac{1}{2} \times \dfrac{1}{25} \times (10) {}^{2}$

$\implies \: s = \dfrac{1}{50} \times 100$

$\implies \: s = 2m$

So, distance travelled in 10 seconds by the body is 2m

Answer 2

Explanation:-

Explanation:-

First let us convert dynes into newton:-

divide the force value by 100000

So 2000 dynes= 0.02 N

So,

F=0.02

Mass=0.5 kg

a=?

Now let's calculate acceleration:-

$\sf\;F=ma\\\\0.02=0.5\times a\\\\0.02=\frac{5a}{10}\\\\0.02=5a\\\\a=0.04\;m/s^2$

So the acceleration is 0.04 m/s²

Now calculate time we will use 2nd equation of motion:-

$\sf\;S=ut+\frac{1}{2}at^2\\\\s=\frac{1}{2}at^2\;\;\;\;\;\;\;(u=0)\\\\s=\frac{1}{2}0.04\times(10)^2\\\\s=0.02\times 100\\\\s=2\/m$

So distance travelled is 2 metres