Question

$\boxed{\Large{\sf Question \:For\:Physicians}}$
A car is weighing 1600kg moving with a velocity of 30m/s retards uniformly coming to rest in 20seconds. Calculate the

(1) initial and final momentum of the car .
(2)Rate of change in
Momentum of the car .
(3) Acceleration of the car

No spams pls​

Answer 1

Answer:

(1) Initial momentum:- 4800 Kgm/s

    Final momentum:- 0

(2) - 240

(3) - 1.5 m/$s^{2}$

Explanation;

Apply all required equations. This is a direct question bro. The requisite equations are given below.

M1VI = Initial Momentum

M2V2 = Final Momentum

m*(v-u)/t = Rate of Change of Momentum

(v-u)/t = Acceleration.

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \: solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{About \: question...}}}}}$

Understanding the question: This question says that we have to find out the initial and final momentum of the car, rate of change in momentum of the car and the acceleration of the car also if a car is weighing 1600 kg moving with a velocity of 30 m/s retards uniformly coming to rest in 20 seconds. Let's do it!

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

$\sf According \: to \: statement \begin{cases} & \sf{Mass \: of \: car \: = \bf{1600 \: kg}} \\ \\ & \sf{Initial \: velocity \: = \bf{30 \: m/s}} \\ \\ & \sf{Final \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Time \: taken \: = \bf{20 \: seconds}} \end{cases}$

Don't be confused! Final velocity cames as zero because car is come to rest!

${\bigstar \:{\pmb{\sf{\underline{To \: calculate...}}}}}$

$\sf According \: to \: statement \begin{cases} & \sf{Initial \: \& \: Final \: momentum} \\ \\ & \sf{Change \: of \: momentum} \\ \\ & \sf{Acceleration} \end{cases}$

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Initial and final momentum of the car are 48000 kg m/s and 0 kg m/s respectively.

⋆ Rate of change in momentum of the car is -2400 kg m/s

⋆ Acceleration of the car is -1.5 m/s²

${\bigstar \:{\pmb{\sf{\underline{Using \: concepts...}}}}}$

⋆ Formula to calculate initial momentum

⋆ Formula to calculate final momentum

⋆ Formula to calculate rate of change in momentum

⋆ Formula to calculate acceleration

${\bigstar \:{\pmb{\sf{\underline{Using \: formulas...}}}}}$

${\small{\underline{\boxed{\sf{p_1 \: = mu}}}}}$

${\small{\underline{\boxed{\sf{p_2 \: = mv}}}}}$

${\small{\underline{\boxed{\sf{Rate \: of \: change \: in \: p = \: \dfrac{p_2 - p_1}{t}}}}}}$

${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

• Where, p denotes momentum, p_1 denotes initial momentum, p_2 denotes final momentum, v denotes final velocity, u denotes initial velocity, t denotes time taken, a denotes acceleration, m denotes mass

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ Firstly let us find out the initial momentum by using formula!

$:\implies \sf p_1 \: = mu \\ \\ :\implies \sf p_1 \: = 1600(30) \\ \\ :\implies \sf p_1 \: = 1600 \times 30 \\ \\ :\implies \sf p_1 \: = 48000 \: kg \: m/s \\ \\ :\implies \sf Initial \: momentum \: = 48000 \: kg \: m/s$

~ Now let us find out the final momentum by using formula!

$:\implies \sf p_2 \: = mv \\ \\ :\implies \sf p_2 \: = 1600(0) \\ \\ :\implies \sf p_2 \: = 1600 \times 0 \\ \\ :\implies \sf p_2 \: = 0 \: kg \: m/s \\ \\ :\implies \sf Final \: momentum \: = 0 \: kg \: m/s$

~ Now let's find out the rate of change in momentum by using formula!

$:\implies \sf \Delta p \: = \dfrac{p_2 - p_1}{t} \\ \\ :\implies \sf \Delta p \: = \dfrac{0-48000}{20} \\ \\ :\implies \sf \Delta p \: = \dfrac{-48000}{20} \\ \\ :\implies \sf \Delta p \: = \dfrac{-4800}{2} \\ \\ :\implies \sf \Delta p \: = -2400 \: kg \: m/s$

~ Now at last let us find acceleration!

$:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{0-30}{20} \\ \\ :\implies \sf a \: = \dfrac{-30}{20} \\ \\ :\implies \sf a \: = \dfrac{-3}{2} \\ \\ :\implies \sf a \: = -1.5 \: m/s^2 \\ \\ :\implies \sf Acceleration \: = -1.5 \: m/s^2$

Don't be confused! Acceleration cames in negative because the car retards!