Question

A bus starts from rest and moving with uniform acceleration attains a velocity of 50 km/h in 3 minutes. Find the acceleration and the distance travelled.

please explain the answer​

Answer 1

Answer :-

→ Acceleration is 0.077 m/s² .

→ Distance travelled is 1247.4 m .

Explanation :-

We have :-

• Initial velocity (u) = 0 m/s

• Final velocity (v) = 50 km/h

• Time taken (t) = 3 mins = 180 sec

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Firstly, let's convert the unit of final velocity of the bus from km/h to m/s .

⇒ 1 km/h = 5/18 m/s

⇒ 50 km/h = 50(5/18)

⇒ 250/18 m/s

⇒ 13.89 m/s

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Now, let's calculate acceleration of the bus by using the 1st equation of motion .

v = u + at

⇒ 13.89 = 0 + a(180)

⇒ 13.89 = 180a

⇒ a = 13.89/180

⇒ a = 0.077 m/s²

Finally let's calculate the distance travelled by the bus using the 2nd equation of motion .

s = ut + ½at²

⇒ s = 0(180) + ½ × 0.077 × (180)²

⇒ s = 0 + (0.5 × 0.077 × 32400)

⇒ s = 0 + 1247.4

⇒ s = 1247.4 m

Answer 2

Answer:

Given :-

• A bus starts from rest and moving with uniform acceleration attains a velocity of 50 km/h in 3 minutes.

To Find :-

• What is the acceleration and the distance travelled.

Formula Used :-

$\clubsuit$ Acceleration Formula :

$\mapsto \sf\boxed{\bold{\pink{a =\: \dfrac{v - u}{t}}}}$

$\clubsuit$ Second Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{s =\: ut + \dfrac{1}{2}at^2}}}$

where,

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

Solution :-

First, we have to convert the time minutes into seconds :

$\implies \sf Time =\: 3\: minutes$

$\implies \sf Time =\: 3 \times 60\: seconds\: \: \bigg\lgroup \small\bold{\pink{1\: minutes =\: 60\: seconds}}\bigg\rgroup$

$\implies \sf \bold{\purple{Time =\: 180\: seconds}}$

Now again, we have to convert final velocity km/h into m/s :

$\implies \sf Final\: Velocity =\: 50\: km/h$

$\implies \sf Final\: Velocity =\: 50 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \small\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Final\: Velocity =\: \dfrac{250}{18}\: m/s$

$\implies \sf\bold{\purple{Final\: Velocity =\: 13.89\: m/s}}$

Now, we have to find the acceleration :

Given :

• Final Velocity (v) = 13.89 m/s
• Initial Velocity (u) = 0 m/s
• Time Taken (t) = 180 seconds

According to the question by using the formula we get,

$\longrightarrow \sf a =\: \dfrac{13.89 - 0}{180}$

$\longrightarrow \sf a =\: \dfrac{13.89}{180}$

$\longrightarrow \sf\bold{\red{a =\: 0.077\: m/s^2}}$

${\small{\bold{\underline{\therefore\: The\: acceleration\: of\: a\: bus\: is\: 0.077\: m/s^2\: .}}}}$

Now, we have to find the distance travelled by a bus :

Given :

• Initial Velocity (u) = 0 m/s
• Time Taken (t) = 180 seconds
• Acceleration (a) = 0.077 m/s²

According to the question by using the formula we get,

$\longrightarrow \sf s =\: (0)(180) + \dfrac{1}{2} \times (0.077)(180)^2$

$\longrightarrow \sf s =\: 0 \times 180 + \dfrac{1}{2} \times 0.077 \times 180 \times 180$

$\longrightarrow \sf s =\: 0 + \dfrac{1}{2} \times 0.077 \times 32400$

$\longrightarrow \sf s =\: 0 + \dfrac{1}{2} \times 2494.8$

$\longrightarrow \sf s =\: 0 + 1247.4$

$\longrightarrow \sf\bold{\red{s =\: 1247.4\: m}}$

${\small{\bold{\underline{\therefore\: The\: distance\: travelled\: by\: a\: bus\: is\: 1247.4\: m\: .}}}}$