Question

A bus starting from rest moves with a uniform acceleration of 0.1 m s-2 for 2 minutes.
Find (a) the speed acquired
(b) the distance travelled.​

Answer 1

Answer:

Given :-

Initial velocity (u) = 0

Acceleration (a) = 0.1ms-2

Time (t) = 2 minute = 120 second

Solution :-

(a) The speed acquired:

We know that, $\boxed{\red{v = u + at}}$

$v = 0 + 0.1 \times 120 \\ = \boxed{\underline{\green{120 \: m/s}}}$

Thus, the bus will acquire a speed of 120 m/s after 2 minute with the given acceleration.

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(b) The distance travelled:

We know that,

$\boxed{\red{s = ut + \frac{1}{2} a {t}^{2}}}$

$s = \: 0 \times 120 + \frac{1}{2} \times 0.1 \times ({120})^{2} \\ \\ = \: \: \: 0 + \frac{1}{2} \times 0.1 \times 14400 \\ \\ = \: \: \: \: \frac{1}{2} \times 1440 \\ \\ = \: \: \boxed{\underline{\green{720}}}$

Thus, bus will travel a distance of 720 m in the given time of 2 minute.

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Answer 2

Given : Initial speed of bus, u 0 m/s & Acceleration of bus, a 0.1 m/s & Time taken by bus, t 60 × 2 => 120 s

To Find : Find the speed required & Distance travelled ?

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Solution : The speed required. Here, we have to find the distance travelled (s)

$~$

$\underline{\frak{As~ we ~know~ that~:}}$

• $\boxed{\sf\pink{v~=~u~+~at}}$★

$~$

=> Then, we use 1st equation of motion that is :

• v = u + at

$~$

Where,

• u = Initial Velocity
• v = Final Velocity
• t = Time
• a = Acceleration
• s = Distance

$~$

$\qquad\qquad{\sf:\implies{v~=~u~+~at}}$

$\qquad\qquad{\sf:\implies{v~=~0~+~0~×~1~×~120}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{v~=~12~m/s}}}}}$★

$~$

Therefore,

• The speed acquired by bus is 12 m/s

$~$

• (a) Distance Travelled

$~$

Here, we use 3rd equation of motion that is :

• v² - u² = 2as

$~$

$\qquad\qquad{\sf:\implies{v^2~-~u^2~=~2as}}$

$\qquad\qquad{\sf:\implies{\bigg(12\bigg)2~-~\bigg(0\bigg)2~=~2\bigg(0.1\bigg)s}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\pink{s~=~720~m}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{Distance~Travelled~by~bus~is~\bf{\underline{720~m}}}}$