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Question

# A body travels 200 cm in the first two seconds and 220 cm in the next 4 seconds with same acceleration. The velocity of the body at the end of the 7th second is:

A
5 cm/s
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B
10 cm/s
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C
15 cm/s
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D
20 cm/s
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Solution

## The correct option is B 10 cm/slet the body have displacement as follows :x=at2+bt+c (a = constant acceleration)as body travels 200cm in first t=2 seconds,⇒x2−x1=(at22+bt2+c)−(at21+bt1+c)⇒200=4a+2b→(1)Similarity it travels 220cm in t1=25 to t2=65⇒220=(a62+b6+c)−(a.22+b.2+c)⇒220=32a+4b→(2)solving (1) & (2) given,a=−152 and b=115Thus, equation of motion for particle,x(t)=−152t2+115t+cand, velocity at t=7 given by:v(t=7)=dxdt|t=7=(−15t+115)t=7=10cm/s

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