Question

19.A train starting from rest,moves with an uniform acceleration of 10m/s, covers50m,

calculate its velocity of travel​

Answer 1

Answer:-

$\pink{\bigstar}$ The velocity of travel will be $\large\leadsto\boxed{\tt\purple{31.62 \: m/s}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Given:-

• Train starts from rest and moves with an uniform acceleration of 10 m/s.

• It covers 50m.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• To Find:-

• The Velocity of travel

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Solution:-

We know,

• Applying 3rd Equation of Motion:-

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{v^2 = u^2 + 2as}}}$

where,

• v = final velocity

• u = initial velocity

• a = acceleration

• s = distance covered

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

here,

• u = 0 [starts from rest]

• a = 10 m/s

• s = 50 m

• Substituting in the Formula:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf v^2 = (0)^2 + 2 \times 10 \times 50$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf v^2 = 0 + 20 \times 50$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf v^2 = 0 + 1000$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf v^2 = 1000$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf v = \sqrt{1000}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ $\bf\pink{v = 31.62 \: m/s}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the final velocity or the travel velocity will be 31.62 m/s [approx.].

Answer 2

Answer:

• Initial Velocity (u) = 0 m/s [As train starts from rest]
• Acceleration (a) = 10 m/s²
• Distance covered (s) = 50 m
• Final Velocity (v) = ?

• Using the Third Equation of Motion :

⇒ v² - u² = 2as

⇒ v² - (0)² = 2 × 10 × 50

⇒ v² - 0 = 1000

⇒ v² = 1000 + 0

⇒ v² = 1000

• Squaring Root both sides

⇒ v = 10√10 or, 31.62 m/s

∴ Velocity of travel is 10√10 or, 31.62 m/s.