Travelling at 40 km/h , a car must be brought to a halt by applying brakes within the next 4.0 m . Given that the car weighs 2000 kg , determine the average force that must be applied to it.

Correct answer: D. 3.1 × 10^4 N Initial velocity, u = 40 km/h = 40 × (5)/(18) m/s = (100)/(9) m/s Final velocity, v = 0 Distance, s = 4.0 m Mass, m = 2000 kg Using the third equation of motion: v^2 - u^2 = 2as 0 - ((100)/(9))^2 = 2a(4.0) a = -(10000)/(81 × 8) = -(1250)/(81) m/s^2 Average retarding force is given by F = m|a| : F = 2000 × (1250)/(81) = (2500000)/(81) N F 30864 N 3.1 × 10^4 N

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Newton's Laws of Motion

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Newton's Laws of Motion

Travelling at 40 km/h , a car must be brought to a halt by applying...

Travelling at

40 \text{ km/h}

, a car must be brought to a halt by applying brakes within the next

4.0 \text{ m}

. Given that the car weighs

2000 \text{ kg}

, determine the average force that must be applied to it.

Options

A $6.2 \times 10^4 \text{ N}$
B $4.0 \times 10^5 \text{ N}$
C $5.6 \times 10^3 \text{ N}$
D $3.1 \times 10^4 \text{ N}$

Correct answer

D. $3.1 \times 10^4 \text{ N}$

Step-by-step solution

Initial velocity,

u = 40 \text{ km/h} = 40 \times \dfrac{5}{18} \text{ m/s} = \dfrac{100}{9} \text{ m/s}

Final velocity,

v = 0

Distance,

s = 4.0 \text{ m}

Mass,

m = 2000 \text{ kg}

Using the third equation of motion:

v^2 - u^2 = 2as

0 - \left(\dfrac{100}{9}\right)^2 = 2a(4.0)

a = -\dfrac{10000}{81 \times 8} = -\dfrac{1250}{81} \text{ m/s}^2

Average retarding force is given by

F = m|a|

F = 2000 \times \dfrac{1250}{81} = \dfrac{2500000}{81} \text{ N}

F \approx 30864 \text{ N} \approx 3.1 \times 10^4 \text{ N}

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