Can anyone answer these question with some explaination or prove. we graph the d

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Can anyone answer these question with some explaination or prove.

 

we graph the distanced d as the y variable versus the time t as the x variable, which of the following graphs might be an accurate representation of Equation (1) in the lab manual? There are many ways to graph the equation d = vet+1/2at^2 . However not all graphs would be linear. Below are Four different ways to graph this equation, which graphs would be linear? A d vs t^2 B. 1/t vs d/t^2 C. 1/d vs 1/t D. t^2/d vs t/d 1. B,C 2. A,B 3. B, D 4. A, C, D 5. A, B, C

Explanation / Answer

1. d=v0*t+at^2/2 as you can see this is a quadratic function. and as t increase, d also increase. d'=v0+a*t d' is the tangent of the graph, and as t increase, d' also, so the tangent also increase. so it must be graph 4. 2. A must be wrong. d=v0*sqrt(t^2)+at^2/2--> not linear. B. d/t^2=v0/t+a/2 so B is correct. C.1/d=1/(v0t+at^2/2)=1/t*(v0+at/2) --> not linear. D. 1=v0*t/d + a*t^2/2d --> linear. so A and D.

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