Question

39) A bus decreases its speed from 90 km/, to 45 km/h in 5 s. Find the acceleration of the bus. a) 1.5 m/s2 ) /s b) 2.0 m/ C) 3.0 m/s m m d) 2.5 m​

Answer 1

Acceleration - Motion

Acceleration is defined as the rate of change in velocity with respect to time. It is measured as metre per second square. In Mathematically,

$\implies \bar{a} = \dfrac{\Delta v}{\Delta t}$

Where, ā denotes acceleration, ∆v denotes change in velocity (v - v₀) and ∆t denotes total time taken or time interval.

As per the question, A bus decreases its speed from 90 km/h to 45 km/h in 5 seconds. It means the initial velocity is 90km/h and the final velocity is 45km/h.

We know that, to convert the unit from km per hour to m per second we have to divide the velocity value by 3.6. [You can also multiply the velocity value by 5/18 to convert the velocity from km per hour to m per second]

∴ Initial velocity, u = 90/3.6 = 25m/s

∴ Final velocity, v = 45/3.6 = 12.5m/s

Now we know that, acceleration is the rate of change in velocity with respect to time. Therefore,

$\implies \bar{a} = \dfrac{\Delta v}{\Delta t} \\ \\ \implies \bar{a} = \dfrac{u - v}{t}$

Now substituting the known values in the above equation/formula, we get:

$\implies \bar{a} = \dfrac{12.5 - 25}{10} \\ \\ \implies \bar{a} = \dfrac{-12.5}{5} \\ \\ \implies \boxed{\bar{a} = -2.5}$

Note: The negative acceleration is also referred to as retardation and the bus is said to be retarding.

Hence, the acceleration of the bus is 2.5m/s², i.e. option (d).

Answer 2

Given :

Here ,

Initial speed ( u) of bus

• = 90 km / h

So,

$\sf \implies{ \frac{90 \times 1000 \: m}{60 \times 60 \: s} }$

$\bf \implies{25 \: m / s}$

Here,

Final speed (v) of bus

• = 45 km/h

So,

$\sf \implies{ \frac{45\times 1000 \: m}{60 \times 60 \: s} }$

$\bf \implies{12.5 \: m / s}$

Here,

Time taken (t) by bus

• = 5 second

To Find :

• Acceleration of the bus

Formula used :

Acceleration =

$\sf \implies{a = \frac{v - u}{t} }$

Solution :

By Using formula of acceleration ,

$\sf \implies{a = \frac{12.5 - 25}{5} }$

$\sf \implies{a = \frac{ - 12.5}{5} }$

$\bf \implies{a = - 2.5 \: m / {s}^{2} }$

Therefore ,

• Acceleration of the bus is -2.5 m/s²

Hence,

• d) - 2.5 m/s² is correct option

Note :

• The negative sign is for retardation

_______________________

Second method to solve this example

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We know that,

$\sf\implies{ \frac{1 \: km}{h}=\frac{5\: }{18}m/s}$

So ,

$\sf\implies{ \frac{90 \: km}{h}=90 \times \frac{5\: }{18}}$

$\sf\implies{ \frac{450}{18}}$

$\bf \implies{25 \: m / s}$

Similarly,

$\sf\implies{ \frac{45 \: km}{h} = 45 \times \frac{5\: }{18}}$

$\sf\implies{ \frac{225}{18}}$

$\bf \implies{12.5 \: m / s}$

Formula used :

$\sf \implies{v = u + at }$

Solution :

Here ,

Initial speed ( u) of bus

• = 90 km / h

Final speed (v) of bus

• = 45 km/h

Time taken (t) by bus

• = 5 second

So,

By using given formula,

$\sf \implies{12.5 = 25 + a \times (5)}$

$\sf \implies{12.5 -25 + a \times (5)}$

$\sf \implies{-12.5 +5a}$

$\sf \implies{a = \frac{ - 12.5}{5} }$

$\bf \implies{a = - 2.5 \: m / {s}^{2} }$.

Therefore ,

• Acceleration of the bus is -2.5 m/s²