If the velocity varies parabolically, how does the acceleration vary?

Category: QuestionsIf the velocity varies parabolically, how does the acceleration vary?
Editor">Editor Staff asked 1 year ago

If the velocity varies parabolically, how does the acceleration vary?
 
(a) Linearly
 
(b) Hyperbolically
 
(c) Parabolically
 
(d) Elliptically
 
I got this question in an online quiz.
 
My question is from Motion in a Straight Line topic in portion Motion in a Straight Line of Physics – Class 11
Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 1 year ago

Correct choice is (a) Linearly
 
To explain I would say: Velocity varies parabolically implies that velocity is of the form at + bt^2. On differentiating the velocity, we get the equation for acceleration. Therefore, a = dv/dt = a+2bt, which is a linear equation. Hence the acceleration varies linearly.