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.


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Answer 1

Answer:

Mass of the motor car, m = 1200 kg

Initial velocity of the motor car, u = 90 km/h = 25 m/s

Final velocity of the motor car, v = 18 km/h = 5 m/s

Time taken, t = 4 s

According to the first equation of motion:

v = u + at

5 = 25 + a (4)

a = ˆ’ 5 m/s2

Negative sign indicates that its a retarding motion i.e. velocity is decreasing.

Change in momentum = mv ˆ’ mu = m (vˆ’u)

= 1200 (5 ˆ’ 25) = ˆ’ 24000 kg m sˆ’1

Force = Mass — Acceleration

= 1200 — ˆ’ 5 = ˆ’ 6000 N

Acceleration of the motor car = ˆ’ 5 m/s2

Change in momentum of the motor car = ˆ’ 24000 kg m sˆ’1

Hence, the force required to decrease the velocity is 6000 N.

(Negative sign indicates retardation, decrease in momentum and retarding force)

Explanation:

Hope this help you

Answer 2

Given :

• Mass of motorcar, m = 1200 kg

• Initial velocity of motorcar, u = 90 kmh⁻¹ = $\sf{90\times\dfrac{5}{18}\;\;kmh^{-1}}$ = 25 ms⁻¹

• Final velocity of motorcar, v = 18 kmh⁻¹ =$\sf{18\times\dfrac{5}{18}\;\;kmh^{-1}}$= 5 ms⁻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

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

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

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

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

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.