A body is moving with uniform acceleration travels 100m and 120 m respectively in 5 sec and 10 sec . What will be the initial velocity of the body?
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Prachipriyadarshani
Micey9210
29.09.2018
Science
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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