Question

The back shelf of a car has a physics textbook on it. The coefficient of static friction of 0.44 between the book and the surface. If the car is initially moving at a speed of 16 m/s, in how short a distance can the car be stopped at constant acceleration without causing the book to slide forward (and hit the driver in the back of the head)? (This is why you should never keep packages on the back shelf of your car.)

Answer 1

Answer:29.68 m

Explanation :  

Given

coefficient of friction \mu =0.44

Car initial speed=16 m/s

The maximum acceleration that book can bear without sliding is \mu g

$a_{max}=0.44\times 9.8=4.312 m/s^2$

using $v^2-u^2=2as$

Final velocity v=0

$-(16)^2=2(-4.31)s$

$s=\frac{256}{2\times 4.312}$

$s=29.68 m$

Answer 2

If the car is initially moving at a speed of 16 m/s, the shortest distance the car will cover at constant acceleration is 29.09 m

How to determine the acceleration

• Coefficient of friction (μ) = 0.44
• Acceleration due to gravity (g) = 10 m/s²

• Acceleration (a) =?

F = ma = μmg

ma = μmg

Cancel m from both side

a = μg

a = 0.44 × 10

a = 4.4 m/s²

How to determine the distance

• Initial velocity (u) = 16 m/s
• Final velocity (v) = 0 m/s
• Deceleration (a) = –4.4 m/s²
• Distance (s) =?

v² = u² + 2as

0 = 16² + (2 × –4.4 × s)

0 = 256 – 8.8s

Collect like terms

0 – 256 = –8.8s

–256 = –8.8s

Divide both side by –8.8

s = –256 / –8.8

s = 29.09 m

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