Question

A4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? a) the 4.0 kg object b) the 1.0 kg object c) Both objects travel the same distance d) It cannot be determined from the information given.

Answer 1

Answer:

Both objects travel the same distance.

(c) is correct option

Explanation:

Given that,

Mass of first object = 4.0 kg

Speed of first object = 2.0 m/s

Mass of second object = 1.0 kg

Speed of second object = 4.0 m/s

We need to calculate the stopping distance

For first particle

Using equation of motion

$v^2=u^2+2as$

Where, v = final velocity

u = initial velocity

s = distance

Put the value in the equation

$0= u^2-2as_{1}$

$s_{1}=\dfrac{u^2}{2a}$....(I)

Using newton law

$a=\dfrac{F}{m}$

Now, put the value of a in equation (I)

$s_{1}=\dfrac{8}{F}$

Now, For second object

Using equation of motion

$v^2=u^2+2as$

Put the value in the equation

$0= u^2-2as_{2}$

$s_{2}=\dfrac{u^2}{2a}$....(I)

Using newton law

$F = ma$

$a=\dfrac{F}{m}$

Now, put the value of a in equation (I)

$s_{2}=\dfrac{8}{F}$

Hence, Both objects travel the same distance.

Answer 2

The two objects traveled the same distance which is equal to $\frac{8}{F}$.

The given parameters;

• mass of the first object, m₁ = 4.0 kg
• speed of the first object, u₁ = 2.0 m/s
• mass of the second object, m₂ = 1 kg
• speed of the second object, u₂ = 4 m/s

The acceleration of each object is calculated as follows;

F = ma

$a = \frac{F}{m} \\\\a_1 = \frac{F}{4} \\\\a_2 = \frac{F}{1} = F$

The distance traveled by each object is calculated as follows before coming to rest;

$v^2 = u^2 - 2as\\\\when \ the \ objects \ come \ to \ rest , \ v = 0\\\\0 = u^2 - 2as\\\\2as = u^2\\\\s = \frac{u^2}{2a} \\\\s_1 = \frac{(2)^2}{2(F/4)} = \frac{(2)^2}{F/2} \\\\s_1 = \frac{2(2)^2}{F} \\\\s_1 = \frac{8}{F} \\\\s_2 = \frac{(4)^2}{2F} \\\\s_2 = \frac{8}{F}$

Thus, we can conclude that the both objects traveled the same distance.

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