Question

The particle is initially moving with a speed of 20m/s after 10s its speed becomes 5m/s. Then find out acceleration of particle and distance covered by particle in 10s

Do this by equations of motion ​

Answer 1

Answer:

2m/s^2 10m

Explanation:

Answer 2

${\underline {\underline {\large {\bf { Given \: Question: } }}}}$

The particle is initially moving with a speed of 20m/s after 10s its speed becomes 5m/s. Then find out acceleration of particle and distance covered by particle in 10s.

${\underline {\underline {\large {\bf { Required \: Solution: } }}}}$

Given:

• Initial velocity (u) $\longrightarrow$ 20m/s

• Time taken (t) $\longrightarrow$ 10 s

• Final velocity (v) $\longrightarrow$ 5m/s

To calculate:

• Acceleration of the particle (a)

• Distance covered by the particle (s)

Calculation:

${\underline {\boxed {\large {\bf {\blue { Acceleration \: of \: the \: particle:–} }}}}}$

By applying the formula of the first equation of motion:

• ${\underline {\boxed {\large {\bf {\pink { v=u + at} }}}}}$

⠀⠀⠀$\bf {⇢ 5 = 20 + a \times 10}$

⠀⠀⠀

⠀⠀⠀

⠀⠀⠀$\bf {⇢ 5 = 20 + 10a}$

⠀⠀

⠀⠀⠀

⠀⠀⠀$\bf {⇢ 10a = 5- 20 }$

⠀⠀

⠀⠀⠀

⠀⠀⠀$\bf {⇢ 10a = -15 }$

⠀⠀

⠀⠀⠀

⠀⠀⠀$\bf {⇢ a =\dfrac{ -15}{10} }$

⠀⠀

⠀⠀⠀

⠀⠀⠀$\bf {⇢ a =\dfrac{ -3}{2} }$

⠀⠀

⠀⠀⠀

⠀⠀⠀$\boxed { \bf {⇢ a = -1. 5m/{s}^{2}}}$

Thus, the acceleration produced by the particle was ${-1. 2m/{s}^{2}}$ ( negative sign indicates retardation).

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${\underline {\boxed {\large {\bf {\blue { Distance \: covered \: by \: the \: particle:–} }}}}}$

According to the second equation of motion:

• ${\underline {\boxed {\large {\bf {\pink { s=ut + \dfrac{1}{2} a{t}^{2} } } } } }}$

⠀⠀$\bf {⇢s= (20 \times 10 ) + \dfrac{1}{2} \times -1.5 \times {10}^{2} }$

⠀⠀⠀

⠀⠀⠀

⠀⠀$\bf {⇢s= 200 + \dfrac{1}{\cancel{2}} \times -1.5 \times \cancel{100} }$⠀⠀

⠀⠀⠀

⠀⠀⠀⠀

⠀⠀$\bf {⇢ s= 200 + ( 1 \times -1.5) \times 50 }$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀$\bf {⇢ s= 200 + (- 1.5) \times 50 }$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀$\bf {⇢ s= 200 + (-75) }$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀$\bf {⇢ s= 200 -75 }$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀$\boxed { \bf {⇢ s = 125m}}$

Therefore, distance covered by particle in 10s is 125m.

⠀⠀⠀⠀⠀⠀

$\rm \blue { So, we \: are \: done!! }$

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