You slam on the brakes of your car in a panic and skid a distance X on a straight, level road. If you had been traveling half as fast under the same road conditions, you would have skidded a distance

The required skidded distance would be one-forth of the distance skidded if the velocity of the car becomes half.

Explanation:

If '' be the velocity of the car where the brakes are slammed on and 'a' be the constant deceleration gained by the car before coming to stop after skidding a distance 'X' at time 't' where final velocity '', then as can be seen from the figure,

If from any arbitrarily chosen point 'O', '' be the distance where the brakes are slammed on and '' be the distance from the same point 'O' where the car stops, then

Now if the car would have been moving with a velocity '' and would have been skidding a distance 'Y', then from the above equation substituting the velocity we can have

So, if the car were moving at half as fast under the same road conditions, it would have skidded by a distance which is one-forth of the present skidded distance.

the answer would be 32*f

the area between the graph and the t axis