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..???

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Answer 1 · 2018-08-07T05:07:17

Please see the explanation below.

The displacement is

#s(t)=-4t^2+2t#

The velocity is the derivative of the displacement

So,

#v(t)=(ds)/dt=-8t+2#

And when the time is #t=1/2s#, the velocity is

#v(1/2)=-8*1/2+2=-4+2=2ms^-1#

The acceleration is the derivative of the velocity

#a(t)=(dv)/dt=-8ms^-2#

The acceleration is constant whaever the value of #t#