Question

in a safety test , a car of mass 1000 kg is driven into a brick wall . its bumper behaves like a spring ( k = 5x10^6 nm ^-1) and is compressed by a distance of 3 cm as the car comes to rest . determine the initial speed of car .

Answer 1

Answer:

• The Initial speed (u) of the car is 5 √(6) m/s

Given:

1. Mass of car (M) = 1000 Kg
2. Spring constant (K) = 5 × 10⁶ N/m
3. Compression (x) = 3 cm = 0.03 m

Explanation:

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This is a case of law of conservation of Energy. The whole energy in the system will be conserved as conservative forces are acting.

Now,

⇒ Decrease in K.E = Increase in Spring P.E

⇒ 1/2 M v² = 1/2 K x²

Here,

• M Denotes Mass of car.
• v Denotes initial velocity.
• K Denotes spring constant.
• x Denotes compression.

Substituting the values,

⇒ 1/2 × 1000 × v² = 1/2 × 5 × 10⁶ × (0.03)

⇒ 1000 × v² = 5 × 10⁶ × (0.03)

⇒ 1000 × v² = 5 × 10⁶ × 3 × 10⁻²

⇒ 1000 × v² = 15 × 10⁽⁶⁻²⁾

⇒ 1000 × v² = 15 × 10⁴

⇒ 10³ × v² = 15 × 10⁴

⇒ v² = 15 × 10⁴ / 10³

⇒ v² = 15 × 10⁴ × 10⁻³

⇒ v² = 15 × 10⁽⁴⁻³⁾

⇒ v² = 15 × 10

⇒ v² = 150

⇒ v = √(150)

⇒ v = √(5 × 5 × 6)

⇒ v = 5 √(6)

⇒ v = 5 √(6) m/s

∴ The Initial speed (u) of the car is 5 √(6) m/s.

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Answer 2

$\huge\underline\mathtt\purple{Answer:-}$

•The initial speed(u)of car is 5 √(6)m/s.