A body, moving in a straight line with an initial velocity of 5ms−1 and a constant acceleration, covers a distance of 30m in the 3rd second. How much distance will it cover in the next 2 seconds?
A
70m
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B
80m
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C
90m
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D
100m
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Solution
The correct option is C90m Distance covered in nth second is given by Sn=u+a(n−12).
Distance covered in 3rd second is given by 30=5+a(3−12), ⇒a=10ms−2.
Distance covered in 4th second is given by S4=5+10(4−12)=40m
and S5=5+10(5−12)=50m ∴ Distance covered in next two seconds =S4+S5=40+50=90m.
Alternate solution:
Distance covered in nth second is given by Sn=u+a(n−12).
Distance covered in 3rd second is given by 30=5+a(3−12), ⇒a=10ms−2.
So, the distance covered in next 2sec will be the difference of distance covered by the body in 5sec and distance covered by body in 3sec
We will find the difference by using formula s=ut+12at2 ⇒(5×5+12×10×52)−(5×3+12×10×32)=(150−60)=90m