Question

A car of mass 1500 kg is moving with the speed of 36 km/h.It is bought to rest by applying breaks in 2s.
a)What is initial and final momentum of car.
b)what is force on car due to breaks.

Answer 1

Given :-

• mass of Car , m = 1500 kg
• initial velocity of Car , u = 36 km h⁻¹ = 10 m s⁻¹
• final velocity of Car , v = 0
• time taken by Car to come to rest , t = 2 s

To find :-

• initial and final momentum of Car
• Force on Car due to breaks

Knowledge required :-

• Formula to calculate momentum

$\orange{\bigstar}\boxed{\sf{p=mv}}$

(where p is the momentum , m is the mass and v is the velocity of any body )

• Formula to calculate Force

$\orange{\bigstar}\boxed{\sf{F=\dfrac{\Delta p}{t}}}$

(where F is the force , Δ p is the change in momentum, and t is the time taken for change in momentum )

Solution :-

Calculating initial momentum ( p₁ ) of Car

Using formula to calculate momentum

$\implies\sf{p_1=m\times u }\\\\\implies\sf{p_1=1500\times 10}\\\\\underline{\underline{\implies\large{\red{\sf{p_1=15000\:\;\; kgms^{-1}}}}}}$

Calculating final momentum ( p₂ ) of Car

Using formula to calculate momentum

$\implies\sf{p_2=m\times v }\\\\\implies\sf{p_2=1500\times 0}\\\\\underline{\underline{\implies\large{\red{\sf{p_2=0 \;\;}}}}}$

Calculating Force ( F ) on the Car due to breaks

Using formula to calculate force

$\implies\sf{F=\dfrac{p_2-p_1}{t}}\\\\\implies\sf{F=\dfrac{0-15000}{2}}\\\\\implies\underline{\underline{\large{\red{\sf{F=-\;7500\;\;N}}}}}$

Hence,

• initial momentum of Car = 15000 kg ms⁻¹
• final momentum of Car = 0
• Force on Car due to breaks = - 7500 N.