Question

A bus decrease its speed from 90km/h to 60km/h in 6s. Find its acceleration of the bus. with explanation​

Answer 1

Answer:

Given :-

• A bus decrease its speed from 90 km/h to 60 km/h in 6 seconds.

To Find :-

• What is the acceleration of the bus.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

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

Solution :-

First, we have to convert the initial velocity and final velocity km/h into m/s :

❒ In case of initial velocity :

$\implies \sf Initial\: Velocity =\: 90\: km/h$

$\implies \sf Initial\: Velocity =\: 90 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Initial\: Velocity =\: \dfrac{450}{18}\: m/s$

$\implies \sf\bold{\purple{Initial\: Velocity =\: 25\: m/s}}$

❒ In case of final velocity :

$\implies \sf Final\: Velocity =\: 60\: km/h$

$\implies \sf Final\: Velocity =\: 60 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Final\: Velocity =\: \dfrac{300}{18}\: m/s$

$\implies \sf\bold{\purple{Final\: Velocity =\: 16.67\: m/s}}$

Now, we have to find the acceleration of the bus :

Given :

• Final Velocity (v) = 16.67 m/s
• Initial Velocity (u) = 25 m/s
• Time Taken (t) = 6 seconds

According to the question by using the formula we get,

$\longrightarrow \sf 16.67 =\: 25 + a(6)$

$\longrightarrow \sf 16.67 =\: 25 + 6a$

$\longrightarrow \sf 16.67 - 25 =\: 6a$

$\longrightarrow \sf - 8.33 =\: 6a$

$\longrightarrow \sf \dfrac{- 8.33}{6} =\: a$

$\longrightarrow \sf - 1.38 =\: a$

$\longrightarrow \sf\bold{\red{a = - 1.38\: m/s^2}}$

Here, the negetive sign indicates that the velocity is decreasing.

${\small{\bold{\underline{\therefore\: The\: acceleration\: of\: the\: bus\: is\: - 1.38\: m/s^2\: .}}}}$

Answer 2

${\large{\bf{\red{\underline{Given :}}}}}$

• Initial speed = 90km/h
• Final velocity = 60km/h
• Time = 6s

${\large{\bf{\red{\underline{To Find:}}}}}$

• Find the acceleration of bus

${\large{\bf{\red{\underline{Solution :}}}}}$

${\clubs{\bf{First \: equation \: of \: motion :}}}$

${\purple{\bigstar{\pink{\boxed{\mathfrak{V = U + at}}}}}}</p><p>$

Here,

V = Initial velocity

U = Final velocity

A = Acceleration

T = Time

${\clubs{\sf{\underline{Now,}}}}$

Convert :

Initial velocity :

${\sf{\cancel{90km/h} \times \frac{5}{\cancel{18} }}}$

${\sf{5 \times 5 }}$

${\sf{\red{25m/s}}}$

Final velocity :

${\sf{\cancel{60km/h} \times \frac{5}{\cancel{18} }}}$

${\sf{3.33m/s \times 5}}$

${\sf{\red{16.67m/s}}}$

Time :

${\sf{\red{6s}}}$

Than,

${\mapsto{\bf{V = u + a (6)}}}$

${\mapsto{\bf{25 = 16.67 + a(6)}}}$

${\mapsto{\bf{16.67 = 25 + (6)a}}}$

${\mapsto{\bf{16.67 - 25 = (6)a}}}$

${\mapsto{\bf{-8.33 = (6)a }}}$

${\mapsto{\bf{A = {\cancel\frac{ - 8.33}{6} }}}}$

${\mapsto{\red{\bf{A = -1.38m/s }}}}$

So,

${\large{\green{\boxed{\underline{\tt{Acceleration = -1.38m/s}}}}}}$

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