Question

A hamster in its ball starts at rest and accelerates to 3ms in 6 seconds.what is the distance travelled

Answer 1

Given

Ball starts from rest .

Final velocity = 3 m/s

Time taken = 6 seconds.

To find

Distance travelled by ball.

Solution ❶

As the ball starts from rest, so it's initial velocity i.e. u = 0 m/s

Using equation of motion :

⇒ a = (v - u)/t

⇒ a = (3 - 0)/6

⇒ 6a = 3

⇒ a = 3/6

⇒ a = 1/2 m/s²

∴ Acceleration of ball = ½ m/s²

Using equation of motion :

⇒ s = ut + ½at²

⇒ s = 0 × 6 + ½(½ × 6²)

⇒ s = 0 + ½(½ × 36)

⇒ s = ½ × 18

⇒ s = 9 m

∴ Distance travelled = 9 m [Answer]

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Solution ❷

As the ball starts from rest, so u = 0

Acceleration of ball = ½ m/s²

Using 3rd equation of motion :

⇒ v² - u² = 2as

⇒ 3² - 0² = 2 × ½ × s

⇒ 9 - 0 = s

⇒ s = 9 m

∴ Distance travelled = 9 m [Answer!]

Answer 2

GIVEN :-

$\bigstar\ \sf{\color{teal} {Initial\ velocity(u) = 0\ m/s}}\\\sf{\color{teal} {(As\ it\ starts\ from\ rest.)}}$

$\bigstar\ \sf{\color{teal} {Final\ velocity(v) = 3\ m/s}}$

$\bigstar\ \sf{\color{teal} {Time(t)=6\ s}}$

TO FIND :-

$\sf{\color{gold} {The\ distance\ travelled.}}$

SOLUTION :-

$\sf{\color{blue} {We\ know,}}$

$\boxed{\sf{\color{red} {v=u+at}}}$

$\sf{\color{blue} {Putting\ the\ known\ values\ :}}$

$\sf{\color{red} {\implies 3=0+a\times 6}}$

$\sf{\color{red} {\implies 3=6a}}$

$\sf{\color{red} {\implies a=\frac{3}{6} }}$

$\sf{\color{red} {\implies a=0.5\ m/s^2}}$

$\sf{\color{blue} {We\ also\ know\ that,}}$

$\boxed{\sf{\color{red} {v^2-u^2=2as}}}$

$\sf{\color{blue} {Putting\ the\ known\ values\ :}}$

$\sf{\color{red} {\implies (3)^2-(0)^2=2\times0.5\times s}}$

$\sf{\color{red} {\implies 9=1\times s}}\\\\\underline{\color{green}{\boxed{\boxed{\sf{\color{red} {\implies s=9\ m}}}}}}$

$\diamond\ \large\underline{\color{blue} {\sf{So,\ the\ distance\ travelled\ is\ 9\ m.}}}$