Question

On a rough horizontal surface, a body of mass 2kg is given a velocity of 10m/s. If the coefficient of friction is 0.2 and \[g = 10m{s^{ - 2}}\], the body will stop after covering a distance of
A. 200m
B. 25m
C. 50m
D. 250m

Answer 1

Hint:A force called friction prevents two surfaces from sliding against one another. The normal force, or the force that is perpendicular to the surfaces, is directly proportional to the frictional force. Mathematically given by $f = \mu N$. Use the equation of motion ${v^2} = {u^2} + 2as$.



Complete answer:
First make a picture of the whole scenario

Here we are considering a body of mass m moving with an acceleration and frictional force opposing its motion. friction is a force that resists the sliding of two surfaces against each other. The frictional force is proportional to the normal force, which is the force that is perpendicular to the surfaces. The coefficient of friction, $\mu $, determines how much friction there is between the two surfaces.
We can define friction as $f = \mu N$ where N is the normal. Normal force is the force exerted by a surface on an object in contact with it. This force is perpendicular to the surface and is responsible for keeping objects in contact with each other. That means $N = mg$ . so, we can also write $f = \mu mg$ . So, from here we can easily find out the acceleration of the body. We acceleration is given by $a = \mu g$ .
Now motion equations can be applied to find out the final answer.
Newton's motion equation says ${v^2} = {u^2} + 2as$ where v is the final velocity, u is the initial velocity and a is acceleration of the body and s= distance travelled. In the end the body will come to rest so the final velocity is zero. Initial velocity is given that is 10 m/s. acceleration is given by $a = \mu g = 0.2 \times 10 = 2$. So, if we now put our values in the motion equation then we get.
${v^2} = {u^2} + 2as$
$or,0 = 100 + 2 \times ( - 2)s$ here we take the acceleration negative because its direction is opposite the direction of velocity.
$or,4s = 100$
$or,s = 25m$
Hence the body will stop after covering $25m$distance.
So, option B is the correct option.

Therefore B is the right answer.

Note: Friction is a force that prevents two surfaces from moving over one another. The normal force—that is, the force that is perpendicular to the surfaces—relates directly to the frictional force. Also given by $f = \mu N$. One of the equations of motion is ${v^2} = {u^2} + 2as$.