Question

A particle is moving in a straight line. Its displacement at time t is given by s=-4t2 + 2t, then its velocity
and acceleration at time t= 1/2 second​

Answer 1

Dear Student,

From Newton’s second law of eqn.

S= 4t^2 + 2t

v= dS/dt

=8t+2

velocity at t=1/2s

=6m/s

a=dv/dt

=8 m/s^2

Cheers!!

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Answer 2

Hie!!

Equation of Displacement as a function of time is given as

s = -4t² + 2t

ds/dt = -8t + 2 ... Equation i

Where ds/dt is the velocity of particle

V = -8t + 2

V at t = 1/2 sec

V = -8(1/2) + 2

V = -4 + 2

V = -2m/s

To Find Acceleration Differentiate Equation i with respect to t we have

d²s/dt² = -8

Where d²s/dt² is the acceleration of the particle.

Acc = -8m/s²

Acceleration At t = 1/2sec is -8m/s²

Here, Acceleration is an independent Function of time.

Note:-

The velocity used here is instantaneous an velocity and the acceleration used here is an instantaneous Acceleration