The graph of position x versus time t represe | vedclass

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Question

(C) The position of the particle is given by the equation $x(t) = a + bt - ct^2$.To find the velocity $v(t)$,we take the first derivative of position

Vedclass · Accepted Answer

$a_{acc} = -2c$

Vedclass · Answer

(C) The position of the particle is given by the equation $x(t) = a + bt - ct^2$.To find the velocity $v(t)$,we take the first derivative of position with respect to time:$v(t) = \frac{dx}{dt} = \frac{d}{dt}(a + bt - ct^2) = b - 2ct$.To find the acceleration $a_{acc}(t)$,we take the derivative of velocity with respect to time:$a_{acc}(t) = \frac{dv}{dt} = \frac{d}{dt}(b - 2ct) = -2c$.Since $c$ is a positive constant,the acceleration is a constant negative value. Thus,the correct expression is $a_{acc} = -2c$.

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