Question

# 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 ms−1 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 ms−1 Final velocity, v=0 Distance s=5100 m Let the acceleration be a. Using, the third equation of motion v2−u2=2as 0−(103)2=2a×5100 ⇒a=−1000×10002.5×100 =−107 ms−2 According to Newton's second law of motion force, F=ma=10−2×107=105 N (ii) Let time be t. Using, the first equation of motion v=u+at 0=103−107t 107t=103 ⇒ t=103107=10−4 s

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