Question

a bullet stops after travelling a distance of X m ,under the action of a uniform retarding force.How far it will go before being stopped by the same force if its velocity is doubled .

Answer 1

hello ....
here is your answer ...

Let the initial velocity of bullet = u
Final velocity of bullet = 0
distance travelled before coming to rest = x

$<b><i><u>using equation of motion </b></i></u>$
v² - u² = 2as
0² = u²+2ax
a = - u²/2x

$<b><i><u>If the initial velocity is doubled </b></i></u>$
v2  -(2u)2  = 2a(x')

0 = 4u2  – [2u2/(2x)](x')

 x' = 4x

so the bullet penetrates 4 times to the penetration of the bullet in the previous case .