Question

a body moving with uniform acceleration covers a distances S1 and S2 in consecutive time intervals t1 and t2 .Prove that acceleration 'a' of the body a = 2{S2/t2 - S1/t1} / (t1+t2)​

Answer 1

Explanation:

Given a body moving with uniform acceleration covers a distances S1 and S2 in consecutive time intervals t1 and t2 .Prove that acceleration 'a' of the body a = 2{S2/t2 - S1/t1} / (t1+t2)

• We need to find the acceleration and let it be A.
• According to the equation of motion we have s = ut + ½ at^2
•                                 So s1 = ut1 + ½ At1^2--------------1
•                          Now v = u + at
•                                       = u + At1
•                            Now s2 = (u + At1)t2 + 1/2 At2^2------2
• Now we need to find the value of A
•                   So multiply equation 1 by t2 and equation 2 by t1
• So we get  s1t2 = ut1t2 + 1/2 At2t1^2 ----------------------3
•             So s2t1 = t1ut2 + At1^2t2 + ½ At2^2t1-----------4
• Subtracting equation 3 – 4 we get
•                           So s1t2 – s2t1 = ½ At2t1^2 – ½ At2^2t1 – A t1^2t2
•                         So s1t2 – s2t1 = - ½ At1^2t2 – ½ At2^2t1
•                                                 = - ½ At1t2 (t1 + t2)
•                     So 2(s2t1 – s1t2) = A t1t2 (t1 + t2)
•                     So A = 2 (s2t1 – s1t2) / t1t2(t1 + t2)
•                     Or A = 2(s2 / t2 – s1 / t1) / (t1 + t2)

Reference link will be

https://brainly.in/question/9817158