Question

A body is moving with uniform acceleration ,and describes 75m in the 6 th second and 115m in the 11 th second .Show that it moves 155m during the 16 th swecond

Answer 1

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Answer 2

According to the given data at two positions,

the equations we get using the formula and on solving them, we will get

-75 = -u - (11/2)a  → 1 multiplying with (-) on both sides

115 = u + (21/2)a → 2

______________

40 = 0 + 5a

______________

Then, acceleration a = 8 m/s² in 1 (eliminating (-))

We get 75 = u + (11/2)8 ⇒ u = 75-44 = 31 m/s

So, initial velocity, u = 31 m/s

So, at 16th second:

S₁₆ = 31 + (16-1/2)8

     = 31 + 31x4

     = 31+124

     = 155 m

Therefore, at 16th second, the body will be at 155 m. Hence, it is proved.