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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/sec
Step 1: Applying equation of motion
Since 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 cm
Total time: t2=2 s+4 s=6 s
s2=ut2+12at22
420=u(6)+12a(6)2
u+3a=70 ....(2)

Step 2: Initial velocity and acceleration
Subtracting eqn(1) from (2)
2a=30a=15 cm/s2
Putting the value of a in equation (1) we get, u=115 cm/s

Step 3: Velocity at the end of 7th second
Velcity at the end of 7th second:
v=u+at =11515×7=10 cm/s

Hence, Option C is correct.

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