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(A) The displacement of the particle is given by $s(t) = -4t^2 + 2t$.The velocity $v(t)$ is the first derivative of displacement with respect to time

Vedclass · Accepted Answer

$-2, -8$

Vedclass · Answer

(A) The displacement of the particle is given by $s(t) = -4t^2 + 2t$.The velocity $v(t)$ is the first derivative of displacement with respect to time $t$:$v(t) = \frac{ds}{dt} = \frac{d}{dt}(-4t^2 + 2t) = -8t + 2$.The acceleration $a(t)$ is the derivative of velocity with respect to time $t$:$a(t) = \frac{dv}{dt} = \frac{d}{dt}(-8t + 2) = -8$.At time $t = \frac{1}{2} 	ext{ s}$:Velocity $v = -8(\frac{1}{2}) + 2 = -4 + 2 = -2$.Acceleration $a = -8$.Thus,the velocity and acceleration are $-2$ and $-8$ respectively.

$A$ particle is moving in a straight line. Its displacement at time $t$ is given by $s = -4t^2 + 2t$. Then its velocity and acceleration at time $t = \frac{1}{2} \text{ s}$ are:

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