A particle moves along a straight line as per equation x 2 = α α t 2 + 2 β β t + γ γ , where x is the distance travelled and α α , β β , γ γ are constants. Its acceleration varies as
Text Solution
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Given x 2 = ( α α t 2 + 2 β β t + γ γ )
∴ ∴ x = ( α α t 2 + 2 β β t + γ γ ) 1/2
v = 
( α α t 2 + 2 β β t + γ γ ) 1/2 (2 α α t + 2 β β )
= ( α α t 2 + 2 β β t + γ γ ) 1/2 ( α α t + β β )
and a = 
( α α t 2 + 2 β β t + γ γ ) 1/2
(2 α α t + 2 β β ) ( α α t + β β ) + ( α α t 2 + 2 β β t + γ γ ) -1/2 ( α α )
= -( α α t 2 + 2 β β t + γ γ ) -3/2 ( α α t + β β ) 2 + α α ( α α t + 2 β β + γ γ ) -1/2
= ( α α t 2 + 2 β β t + γ γ ) -3/2 – ( α α 2 t 2 – α α 2 – 2 α α β β t + α α 2 t 2 + 2 α α β β t + α α γ γ )
= 
Thus a ∝ ∝ x -3
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