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Derivation of Velocity-Time Relation by Graphical Method

Question. A p...

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Question. A particle is moving in a straight line as per equation x = 4(t -5) + 2(t -5)², then slope of velocity-time graph for particle will be

(a) Increasing with time
(b) Decreasing with time
(c) Constant but negative
(d) Constant but positive

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Solution

Dear Student,

$x = 4 (t - 5) + 2 {(t - 5)}^{2} f i r s t f i n d t h e f u n c t i o n o f v e l o c i t y v = \frac{d x}{d t} = 4 (t - 5) + 4 v = 4 (t - 5) + 4 t o f i n d t h e s l o p e o f v - t d i f f e r e n t i a t e t h e a b o v e e q n a = \frac{d v}{d t} = 4 s o t h e s l o p e i s + v e b u t i t r e m a i n c o n s \tan t . R e g a r d s$

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Figure

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Derivation of Velocity-Time Relation by Graphical Method

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