Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

Options

A.
B.
C.
D.

Answer

c

Explanation

As it is given that the acceleration is constant andn in negative direction velocity is in positive direction. The acceleration and velocity are related as :
`a =(dv)/(dt) " "……(i)`
Taking acceleration to be equal to a negative constant - K .
` - K = (dv)/(dt)`
`dv = - Kt`
integrating both sides .
`int dv = - K int dt`
`v = - Kt + C`
None of the graphs given in the options satisfy the above derived relation between the velocity and the time.
Multiplying dx in numerator annd denominator in equation (i).
`a = (dv)/(dt) xx (dx)/(dx) = (dv)/(dx) xx (dx)/(dt) = v(dv)/(dx)`
`vdu = - kdx`
Intergrating both side .
`int vdv = int - Kdx`
`(v^(2))/(2) = - Kx + c`
`rArr " "x = (C)/(K) - (v^(2))/(2k)`
The graph given in option (c) is not accordance with the above dervied relation.