Question

The motion of a Particle among
is described by the function.
s=6+4+t²-t⁴in S.I unit find the velocity acceleration at t=2 sec​

Answer 1

Answer :

Velocity at t = 2 sec is -24 m/s .

Acceleration at t = 2 sec is -46 m/s² .

Solution :

• Note : If the displacement s is a function of time t , then the instantaneous velocity is given as , v = ds/dt and the instantaneous acceleration is given as , a = dv/dt = d²s/dt² .

Here ,

Displacement , s = 6 + 4t + t² - t⁴

Thus ,

The instantaneous velocity will be given as ;

=> v = ds/dt

=> v = d(6 + 4t + t² - t⁴)/dt

=> v = d6/dt + 4dt/dt + dt²/dt - dt⁴/dt

=> v = 0 + 4 + 2t - 4t³

=> v = 4 + 2t - 4t³

Now ,

The instantaneous velocity at t = 2 sec will be ;

=> v = 4 + 2•2 - 4•2³

=> v = 4 + 4 - 32

=> v = -24 m/sec

Also ,

The instantaneous acceleration will be given as ;

=> a = dv/dt

=> a = d(4 + 2t - 4t³)/dt

=> a = d4/dt + 2dt/dt - 4dt³/dt

=> a = 0 + 2 - 4•3t²

=> a = 2 - 12t²

Now ,

The instantaneous acceleration at t = 2 sec will be ;

=> a = 2 - 12•2²

=> a = 2 - 48

=> a = -46 m/sec²

Hence ,

Velocity at t = 2 sec is -24 m/s .

Acceleration at t = 2 sec is -46 m/s² .