Question

A car travelling with uniform velocity accelerated with constant acceleration.In the fourth second after the acceleration started the car travelled 23 m. In the eighth second it travelled 45m. Use this information to find the initial speed of the car and the magnitude of the acceleration​

Answer 1

 Answer:

         a = 5.5 ms⁻²

        u = 3.75ms⁻¹

Explanation:

In the beginning u = v

when the car accelerated

a = ?  ,  S₄ = 23m ,  u = ?

Sₙ = u + a/2(2n - 1)  (where n is the given second)

23 = u + a/2 (2×4 - 1)

23 = u + a/2 (8 - 1)

23 = u + a/2 (7)

23 = u + 7a/2  -----{i}

45 = u + a/2 (2×8 - 1)

45 = u + a/2 (16 - 1)

45 = u + a/2 (15)

45 = u + 15a/2  -----{ii}

{ii} - {i}

45 - 23 = u + 15a/2 - [ u + 7a/2 ]

22 = u + 15a/2 - u - 7a/2

22 = 15a/2 - 7a/2

22 = 8a/2

8a = 44

a = 44 / 8

a = 5.5 ms⁻²

from {i}

23 = u + 7a/2

23 = u + 7×5.5 / 2

23 = u + 38.5 / 2

23 = u + 19.25

u = 23 - 19.25

u = 3.75ms⁻¹

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