Question

7. A 4 kg mass moving with speed 2 m/s, and a 2 kg mass moving with a speed of 4 m/s, are gliding over a
horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their
motion, and are brought to rest by it. Which statement best describes their respective stopping distances?
(1) The 4 kg mass travels twice as far as the 2 kg mass before stopping
12) The 2 kg mass travels twice as far as the 4 kg mass before stopping
(3) Both masses travel the same distance before stopping
(4) The 2 kg mass travels greater than twice as far​

Answer 1

Answer:

option 2 is correct as the speed 2kg mass is twice than 4kg mass

Answer 2

ANSWER:

(2) The 2 kg mass travels twice as far as the 4 kg mass before stopping

EXPLANATION:

Let us take the speed of the 4 kg mass as 2 m/sec and the 2 kg mass as 4 m/sec

The force developed by the opposing force in opposite direction can be taken as

$F=m a$

$F=m \frac{v^{2}}{2 S}$

The mass is taken as 4 and 2 respectively along with their velocities as 2 m/sec and the 2 kg mass as 4 m/sec

$\frac{F=4 \cdot \frac{2.2}{2 . S_{1}}}{F=2 \cdot \frac{4.4}{2 . S_{2}}}$

$\frac{1=\frac{8}{S_{1}}}{1=\frac{16}{S_{2}}}$

$S_{1} / S_{2}=1 : 2$

Therefore, the distance covered by the 2 kg mass is twice than that of the 4 kg mass.