Question:
A car can be stopped over a distance x when its momentum is P .What will be the stopping distance when momentum is 2P
Answer:
When the momentum is P, the distance covered by car= x
P= mV ......(1)
Here, m is mass of car,which is constant
V is velocity of car.
From equation (1),initial Velocity of car V= P/m
The car is finally stopped,so final velocity of car is 0.
Using the third equation of motion
v2 -u2 = 2×a×x
a is acceleration
(0)2 -(P/m)2 = 2×a.x
So, a = -P2 /2m2x .....(2)
In second case, when the momentum of car= 2P
the initial velocity of car will be ,v= 2P/m
Final velocity is again 0.
Using the third equation of motion
v2 -u2 = 2×a.s
s is distance covered when momentum= 2P
(0)2 -(2P/m)2 = 2×a.s
s= 4x
So, the distance covered by car will be 4 times,when the momentum doubled.
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