Question

A bus running
at a speed of 18 km/h is stopped in 2.5 second by
applying brakes. Calculate the retardation
produced​

Answer 1

Given :

• Initial velocity (u) = 18 km/h

• Time Taken = 2.5 s

To find :

The Retardation Produced by the bus .

Solution :

Let us first convert Initial Velocity from km/h to m/s.

We know that to convert the unit from km/h to m/s , we have to multiply it by 5/18 i.e,

x km/h = (x × 5/18) m/s

Now by using the above equation and substituting the value of x in it , we get :

➝ 18 km/h = (18 × 5/18) m/s

⠀⠀⠀⠀⠀⠀⠀= (1 × 5) m/s

⠀⠀⠀⠀⠀⠀⠀= 5 m/s

Hence the initial velocity of the bus in m/s is 5 m/s.

Now,

To find the Retardation Produced by the bus :

We know the first Equation of the motion i.e,

$\boxed{\bf{v = u + at}}$

Where :

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

Now using the first Equation of Motion and substituting the values in it, we get :

$:\implies \bf{v = u + at}$

$:\implies \bf{0 = 5 + a \times 2.5}$

[Note : Here the final Velocity will be Zero , (i.e, v = 0 m/s) since , the car is at rest after applying the before]

$:\implies \bf{0 = 5 + 2.5a}$

$:\implies \bf{-5 = 2.5a}$

$:\implies \bf{\dfrac{-5}{2.5} = a}$

$:\implies \bf{\dfrac{-50}{25} = a}$

$:\implies \bf{-2 = a}$

$\boxed{\therefore \bf{a = -2\:ms^{-2}}}$

Hence, the acceleration produced by the bus is -2 m/s² or the Retardation Produced is 2 m/s².

Answer 2

Answer:

Here, u = 18 km/h = 5 m/s

v = 0 m/s

t = 2.5 s

a = ?

So, By using the formula of motion, we get,

v = u + at

0 = 5 + a × 2.5

-5 = a × 2.5

-5/2.5 = a

-2 = a

Therefore, the retardation is 2 ms^-2. Note: Minus sign indicates negative direction.