Question

A motorcar of mass 1200 kg is moving along a straight line
with a uniform velocity of 90 km/h. Its velocity is slowed down
to 18 km/h in 4 s by an unbalanced external force. Calculate
the acceleration and change in momentum. Also calculate the
magnitude of the force required.

spammers immediately reported.....

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Answer 1

Given :

Mass of motorcar, m = 1200 kg

Initial velocity of motorcar, u = 90 kmh⁻¹ =

$\sf{90\times\dfrac{5}{18}\;\;kmh^{-1}}$

Final velocity of motorcar, v = 18 kmh⁻¹

$\sf{18\times\dfrac{5}{18}\;\;kmh^{-1}}$

Time in which motorcar is slowed down, t = 4 s

To find :

Acceleration of the Motorcar, a =?

Change in momentum, Δ p =?

Magnitude of force for slowing down the motorboat, F =?

Formulae required :

the First equation of motion

$\red{\bigstar}\boxed{\sf{v=u+at}}★$

Formula to calculate change in momentum

$\red{\bigstar}\boxed{\sf{\Delta\;p=p_f-p_i=mv-mu}}★$

Formula to calculate Force required

$\red{\bigstar}\boxed{\sf{F=\dfrac{\Delta\;p}{t}}}★$

[ Where v is final velocity, u is initial velocity, a is acceleration, t is time taken, Δ p is change in momentum, $\sf{p_i}$

is initial momentum, $\sf{p_f}$

is final momentum, F is force required and m is mass of body ]

Solution :

Calculating acceleration of motorboat

Using first equation of motion

$\implies\sf{5=25+a\times 4}⟹$

$\implies\sf{4a=-20}⟹$

$\implies\underline{\underline{\red{\sf{a=-5\;\;ms^{-2}}}}}⟹$

Calculating change in momentum

Using formula for change in momentum

$\implies\sf{\Delta\;p=p_f-p_i=mv-mu}⟹$

$\implies\sf{\Delta\;p=1200\times 5 -}$

$\implies\sf{\Delta\;p=1200\times 5 - 1200 \times 25}⟹$

$\implies\underline{\underline{\red{\sf{\Delta\;p=-24000\;\;Kgms^{-1}}}}}$

Calculating the magnitude of force required

Using formula for calculating force

$\implies\sf{F=\dfrac{\Delta\;p}{t}}⟹$

$\implies\sf{F=\dfrac{-24000}{4}}$

$\implies\underline{\underline{\red{\sf{F=-6000\;\;J}}}}⟹$

Therefore,

Acceleration of motorboat is -5 m/s².

Momentum is reduced by 24000 kg ms⁻¹.

Magnitude of force required is 6000 J.

Answer 2

Answer:

mass of car=1200kg

initial velocity (u)=90km/h =90×5/18=25m/s

final velocity (v)=18km/h=18×5/18=5m/s

time=4 seconds

Now,

acceleration (a)=(v-u)/t

=5-25/4

=-20/4

=-5m/s²

change in momentum=final momentum-initial momentum

=mv-mu =m(v-u)

=1200(5-25)

=1200×(-20)=-24000 kg m/s

Force=ma

=1200kg×(-5m/s²)

=-6000 Newton

negative sign implies that the force is applied In the opposite direction .