a body is moving with a uniform acceleration and describes 75 m in 6th second and 115 metre in 11th second show that its moves 150m during the 16th second
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Formula used: Sₓ=u+a(n-1/2)
To find the acceleration:
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.
To find the acceleration:
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.
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