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Question

# A body covers 200cm in the first 2 sec.and 220cm in next 4 sec. What is the velocity of the body at the end of 7th second

A
40cm/sec
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B
20cm/sec
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C
10cm/sec
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D
5cm/sec
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Solution

## The correct option is C 10cm/secStep 1: Applying equation of motionSince acceleration is constant, therefore we can apply equation of motion.In first case: When body covers 200cm in 2s:s1=ut1+12at21⇒ 200=u(2)+12a(2)2⇒ a+u=100 ....(1)In second case: Total displacement, s2=200 cm+220 cm=420 cmTotal time: t2=2 s+4 s=6 ss2=ut2+12at22⇒420=u(6)+12a(6)2⇒ u+3a=70 ....(2)Step 2: Initial velocity and accelerationSubtracting eqn(1) from (2)2a=−30⇒a=−15 cm/s2Putting the value of a in equation (1) we get, u=115 cm/sStep 3: Velocity at the end of 7th secondVelcity at the end of 7th second:v=u+at =115−15×7=10 cm/sHence, Option C is correct.

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