# A particle is moving in a straight line.its displacement at time t is given by s (in m) =-4t^2+2t,then its velocity and acceleration at time t=1/2 second are..???

Aug 7, 2018

#### Explanation:

The displacement is

$s \left(t\right) = - 4 {t}^{2} + 2 t$

The velocity is the derivative of the displacement

So,

$v \left(t\right) = \frac{\mathrm{ds}}{\mathrm{dt}} = - 8 t + 2$

And when the time is $t = \frac{1}{2} s$, the velocity is

$v \left(\frac{1}{2}\right) = - 8 \cdot \frac{1}{2} + 2 = - 4 + 2 = 2 m {s}^{-} 1$

The acceleration is the derivative of the velocity

$a \left(t\right) = \frac{\mathrm{dv}}{\mathrm{dt}} = - 8 m {s}^{-} 2$

The acceleration is constant whaever the value of $t$