Question

${\large{\red{\pmb{\mathfrak{\underline{Question :-}}}}}}\ \textless \ br /\ \textgreater$
An electron moving with a velocity of 5 * 10 power 4 m/s enters with a uniform acceleration of 10 power 4m/s-² in the direction of initial motion.

Calculate :
i)Calculate the time in which the electron would acquires a velocity double to its initial velocity.
ii)How much distance electron would cover in this time.

❒Note :-
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Answer 1

Answer :-

Given:-

An electron moving with a velocity of 5 × 10⁴ m/s enters with a uniform acceleration of 10⁴ m/s² in the direction of initial motion.

To find:-

The time in which the electron would acquires a velocity double to its initial velocity.

How much distance electron would cover in this time.

Solution:-

⇒ Initial velocity (u) = 5 × 10⁴ m/s

⇒ Acceleration (a) = 10⁴ m/s

ATP :-

⇒ Final velocity (2u) = 2 × 5 × 10⁴ m/s

• 10 × 10⁴ m/s

Using Kinematics:

⇒ v = u + at

⇒ t = u - u/a

• 10 × 10⁴ - 5 × 10⁴/10⁴
• 5 × 10⁴/10⁴
• 5 s

Using Kinematics:

⇒ s = ut + 1/2 at²

• 5 × 10⁴ × 5 + 1/2 (10⁴)(5)²
• 37.5 × 10⁴ m

Answer 2

$\huge \fbox \purple{Answer✪}$

$\textbf{Given:-}$

$\sf \colorbox{pink} {➥Initial Velocity \: u} = 5 \times {10}^{4} m {s}^{ - 1}$

$\sf \colorbox{pink} {➥Acceleration \: a = } {10}^{4} m \: {s}^{ - 2}$

$\textbf{(i) Final Velocity}$

$⇒\sf \colorbox{god} {v = 2u(given)}$

$⇒\sf \colorbox{god} {v = 2} \times 5 \times {10}^{4} m \: {s}^{ - 1} \\ \: \: \: \: \: \: = 10 \times {10}^{4} \sf \colorbox{god} {}m \: {s}^{ - 1}$

$⇒\sf \colorbox{god} {v = u + at}$

$⇒\sf \colorbox{god} {t = } \frac{v - u}{a}$

$\textbf{Substituting the values, we get}$

$︎\sf \colorbox{god} {t = } \left( \frac{10 \times {10}^{4} - 5 \times {10}^{4} }{ {10}^{4} } \right) \] = \frac{5 \times {10}^{4} }{ {10}^{4} }$

$\sf \colorbox{god} { = 5 \: sec}$

$\sf \colorbox{god} {(ii) \: \: \: \: \: \: \: \: \: s = ut + } \frac{1}{2} {at}^{2}$

$\textbf{Where initial Velocity}$

$➥\sf \colorbox{lightgreen} {u = 5} \times {10}^{4} m \: {s}^{ - 1}$

$➥\sf \colorbox{lightgreen} {Acceleration} a = {10}^{4} m \: {s}^{ - 2}$

$➥\sf \colorbox{lightgreen} {Time t = 5 sec}$

$\textbf{Substituting the values, we get}$

$⇒\sf \colorbox{god} {s = }(5 \times {10}^{4} ) \times 5 + \frac{1}{2} ( {10}^{4} ) \times (5 {)}^{2}$

$⇒25 \times {10}^{4} + \frac{25}{2} \times {10}^{4}$

$︎ \: \fbox{37.5×10⁴m}$

$\\ \\ \\ \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙ⌨}$