Question

A car is moving with a uniform velocity of 30 ms-1. It is stopped in 2s by applying a force of 1500 N through its brakes. Calculate : a) the change in momentum of car b) the retardation produced in car and c) the mass of car

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Answer 1

Answer:

Given :-

• A car is moving with a uniform velocity of 30 m/s. It is stopped in 2 seconds by applying a force of 1500 N through its brakes.

To Find :-

1. What is the change in momentum of car
2. What is the retardation produced in car
3. What is the mass of car

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

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

$\clubsuit$ Mass Formula :

$\mapsto \sf\boxed{\bold{\pink{m =\: \dfrac{F}{a}}}}$

where,

• m = Mass
• F = Force
• a = Acceleration

$\clubsuit$ Change in Momentum Formula :

$\footnotesize\mapsto\sf\boxed{\bold{\pink{Change\: in\: Momentum =\: mv - mu}}}$

where,

• m = Mass
• v = Final Velocity
• u = Initial Velocity

Solution :-

First, we have to find the retardation produced in car :

Given :

★ Final Velocity (v) = 0 m/s

★ Initial Velocity (u) = 30 m/s

★ Time Taken (t) = 2 seconds

According to the question by using the formula we get,

$\longrightarrow \sf\bold{\purple{v =\: u + at}}$

$\longrightarrow \sf 0 =\: 30 + a(2)$

$\longrightarrow \sf 0 - 30 =\: 2a$

$\longrightarrow \sf - 30 =\: 2a$

$\longrightarrow \sf \dfrac{- \cancel{30}}{\cancel{2}} =\: a$

$\longrightarrow \sf \dfrac{- 15}{1} =\: a$

$\longrightarrow \sf - 15 =\: a$

$\longrightarrow \sf\bold{\red{a =\: - 15\: m/s^2}}$

As we know that :

• Retardation is a negetive acceleration.

Here, negetive sign indicates retardation.

${\small{\bold{\underline{\therefore\: The\: retardation\: produced\: in\: car\: is\: - 15\: m/s^2\: .}}}}$

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Now, we have to find the mass of car :

Given :

★ Force (F) = 1500 N

★ Acceleration (a) = 15 m/s²

According to the question by using the formula we get,

$\longrightarrow \sf\bold{\purple{Mass =\: \dfrac{Force}{Acceleration}}}$

$\longrightarrow \sf Mass =\: \dfrac{\cancel{1500}}{\cancel{15}}$

$\longrightarrow \sf Mass =\: \dfrac{100}{1}$

$\longrightarrow \sf\bold{\red{Mass =\: 100\: kg}}$

${\small{\bold{\underline{\therefore\: The\: mass\: of\: car\: is\: 100\: kg\: .}}}}$

____________________________________

Now, we have to find the change in momentum :

Given :

★ Mass (m) = 100 kg

★ Final Velocity (v) = 0 m/s

★ Initial Velocity (u) = 30 m/s

According to the question by using the formula we get,

$\small\longrightarrow \sf\bold{\purple{Change\: in\: momentum =\: mv - mu}}$

$\small\longrightarrow \bf Change\: in\: momentum =\: m(v - u)$

$\small\longrightarrow \sf Change\: in\: momentum =\: 100(0 - 30)$

$\small\longrightarrow \sf Change\: in\: momentum =\: 100(- 30)$

$\small\longrightarrow \sf Change\: in\: momentum =\: 100 \times (- 30)$

$\small\longrightarrow \sf\bold{\red{Change\: in\: momentum =\: - 3000\: kg\: m/s^2}}$

${\small{\bold{\underline{\therefore\: The\: change\: in\: momentum\: of\: car\: is\: -3000\: kg\: m/s^2\: .}}}}$

Answer 2

Answer:

above is your answer

Explanation:

hope it helps!!