Question

A speeding car changes its velocity from 108 kmh-1 to 36kmh-1 in 4s. Calculate its deceleration in a) ms-2 b)kmh-2

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Deceleration=5\:m/s^{2}}}}$

$\green{\tt{\therefore{Deceleration=64800\:km/h^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: velocity(u) = 108 \: km /h \\ \\ \tt: \implies Final \: velocity(v) = 36 \: km /h \\ \\ \tt: \implies Time(t) = 4 \: sec \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Deceleration \: of \: car =?$

• According to given question :

$\tt \circ \: u = 108 \times \frac{5}{18} = 30 \: m/s \\ \\ \tt \circ \: v = 36 \times \frac{5}{18} = 10 \: m/s \\ \\ \tt \circ \: t = 4 \: sec\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 10 = 30 + a \times 4 \\ \\ \tt: \implies 10 - 30 = a \times 4 \\ \\ \tt: \implies a = \frac{ - 20}{4} \\ \\ \green{\tt: \implies a = - 5 \: {m/s}^{2} } \\ \\ \green{\tt \therefore Deceleration \: of \: car \: is \: 5 \: m/ {s}^{2} } \\ \\ \bold{For \: deceleration \: in \: km/ h^{2}} \\ \tt: \implies Deceleration = 5 \times 12960 \\ \\ \green{\tt: \implies Deceleration =64800\: {km/h}^{2} }$

Answer 2

Given :-

A speeding car changes it's velocity from 108 km/hr to 36 km/hr in 4 seconds

Required to find :-

• Calculate the deceleration in m/s and km/hr

Formula used :-

$\Large{\leadsto{\boxed{\rm{ Acceleration = \dfrac{ v - u }{ t } }}}}$

Solution :-

Given information :-

A speeding car changes it's velocity from 108 km/hr to 36 km/hr in 4 seconds

we need to find the deceleration of the car in km/hr and m/s

From the given information we can conclude that ;

• Initial velocity of the car ( u ) = 108 km/hr

• Final velocity of the car ( v ) = 36 km/hr

• Time ( t ) = 4 seconds

we need to convert this time into hours ;

So,

1 second = 1/3600 hour

4 seconds = ? hours

=> 4 x 1/3600

=> 1/900 hrs

Using the formula ,

$\Large{\leadsto{\boxed{\rm{ Acceleration = \dfrac{ v - u }{ t } }}}}$

By, substituting the values we get ;

$\rightarrowtail{\rm{ Acceleration = \dfrac{ 36 - 108 }{ \dfrac{1}{900} } }}$

$\rightarrowtail{\rm{ Acceleration = \dfrac{ - 72 \times 900 }{ 1 } }}$

$\rightarrowtail{\rm{ Acceleration = - 64,800 \; km/h{r}^{2} }}$

$\rm{ \big( \because \; Negative \; acceleration \; is \; retardation \big)}$

Hence,

• Retardation ( in km/hr ) = - 64,800 km/hr²

Now, we need to find the retardation of the car in m/s²

So,

let's convert the initial and final velocity into m/s from km/hr .

1 km/hr = 5/18 m/s

108 km/hr = ? m/s

=> 108 x 5/18

=> 6 x 5

=> 30 m/s

108 km/hr = 30 m/s

Similarly,

36 km/hr = ? m/s

=> 36 x 5/18

=> 2 x 5

=> 10 m/s

36 km/hr = 10 m/s

This implies,

• Initial velocity of the car ( in m/s ) = 30 m/s

• Final velocity of the car ( in m/s ) = 10 m/s

• Time = 4 seconds

Using the above formula ,

$\tt{ a = \dfrac{ 10 - 30 }{ 4 } }$

$\tt{ a = \dfrac{ - 20 }{ 4 } }$

$\tt{ a = - 5 \; m/{s}^{2} }$

Therefore,

• Retardation ( in m/s ) = - 5 m/s²