a car of mass 500 kg moving with the 72 kilometre per hour how much force is required to stop the car within 100 metre
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a car of mass 500 kg moving with the 72 kilometre per hour how much force is required to stop the car within 100 metre
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Verified answer
Mass of the car (m) = 500 kg
Initial velocity of the car (u) = 72 km/h = 20 m/s
★ 1 km/h = ⁵/₁₈ m/s
As it stops finally , so
Final velocity of the car (v) = 0 km/h = 0 m/s
Distance moved by the car (s) = 100 m
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Force (F) : It is defined as mass times the acceleration . SI unit is Newton .
➳ F = m × a
3rd equation of motion :
➳ v² - u² = 2as
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➠ v² - u² = 2as
➠ (0)² - (20)² = 2a(100)
➠ 0 - 400 = 200a
➠ 200a = -400
➠ a = - 2 m/s²
Note : - ve sign of acceleration denotes retardation
[tex]:\implies \sf F=ma[/tex]
[tex]:\implies \sf F=(500)(-2)[/tex]
[tex]:\implies \sf{\bf{\pink{F=-1000\ N}}}\ \; \bigstar[/tex]
Note : - ve sign of force denotes retarding force
Magnitude of the force = 1000 N
Answer:
[tex]\underline{\bigstar\:\textsf{Using Third Equation of Motion :}}[/tex]
[tex]:\implies\sf v^2-u^2=2as\\\\\\:\implies\sf (0)^2-(72\:km/h)^2=2 \times a \times 100\:m\\\\\\:\implies\sf -\:\bigg(72 \times \dfrac{5}{18}\:m/s\bigg)^2=2 \times a \times 100\:m\\\\\\:\implies\sf -\:(4 \times 5\:m/s)^2 = 2 \times a \times 100\:m\\\\\\:\implies\sf - \:(20\:m/s)^2 = 2 \times a \times 100\:m\\\\\\:\implies\sf - \:400 \:m^2/s^2 = 200 \:m \times a\\\\\\:\implies\sf \dfrac{- \:400 \:m^2/s^2}{200 \:m} = a\\\\\\:\implies\sf a = - \:2 \:m/s^2[/tex]
[tex]\rule{180}{1.5}[/tex]
[tex]\underline{\bigstar\:\textsf{Using formula for Force :}}[/tex]
[tex]:\implies\sf Force = Mass \times Acceleration\\\\\\:\implies\sf Force=500\:kg \times -\:2\:m/s^2\\\\\\:\implies\sf Force=-\:1000\:kg\:m/s^2\\\\\\:\implies\underline{\boxed{\sf Force=-\:1000\:N}}[/tex]
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[tex]\therefore\:\underline{\textsf{It'll take \textbf{- 1000 N} to stop car within 100 metres}}.[/tex]