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Micey9210

29.09.2018

Science

Secondary School

+13 pts

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A body moving with UNIFORM ACCELERATION covers 100m in the first 10 seconds and 150m in the next 10 sec. Then the initial velocity of the body is?

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Deekshitha18Ambitious

t1 ≈ 10 sec

by USING equation of motion, s = ut + (1/2) at²we get

100 = u x 10 + (1/2) a (10)² = 100

100 = u x 10 + (1/2 ) x a x 10 x 10

= 100 = 10{u + (1/2) x a x 10)

= 100/10 = u + 5a

= 10 = u+5 a .........(1)

to find initial velocity for second case we use first equation of motion v = u + at on first motion we get v = u + a x 10 = v = u + 10a

Using second equation of motion s = ut + (1/2) gt² for second motion we get

150 = (u + 10a)x10 + (1/2) a (10)² = 150 = 10X(u + 10a) + (1/2) g x10x10

= 150 = 10 {(u +10a) + (1/2) x 10 x a} = 150/10 = u + 10a + 5a

= 15 = u + 15a= u + 15a = 15 ......(2)

Now subtracting equation (1) from equation (2) we get

u + 15a - (u + 5a) = 15 - 10 = u + 15a - u - 5a = 5

= u - u + 15a - 5a = 5

= 10a = 5 = a = 5/10

= a = 1/2

substituting this value of a in equation (1) we get

u + 5 x (1/2) = 10 = u + (5/2) = 10

= u = 10 - 5/2 = 10 - 2.5

= u = 7.5 m/s