a body moving with a uniform acceleration covers 100m in first 10seconds and 150m inthe next 10 seconds.the inintial velocity of the body is ?.
Answers
Using second equation of motion s = ut + (1/2) at² we get 100 = u x 10 + (1/2) a (10)² = 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 ( rearranging equation) = u + 5a = 10 .........(1) Thus 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 Now this will be our initial velocity for second motion 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 (rearranging equation) = 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 (rearranging equation) = 10a = 5 = a = 5/10 = a = 1/2 Putting 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