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Question 18
Using second law of motion, derive the relation between force and acceleration. A bullet of 10 g strikes sand-bag at a speed of 103 ms1 and gets embedded after travelling 5 cm. Calculate

(i) the resistive force exerted by the sand on the bullet
(ii) the time taken by the bullet to come


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Solution

(i) Mass, m=10g=101000 kg

Initial velocity, u=103 ms1

Final velocity, v=0

Distance s=5100 m
Let the acceleration be a.

Using, the third equation of motion

v2u2=2as

0(103)2=2a×5100

a=1000×10002.5×100

=107 ms2

According to Newton's second law of motion force, F=ma=102×107=105 N

(ii) Let time be t.

Using, the first equation of motion

v=u+at

0=103107t

107t=103

t=103107=104 s

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