Question

If s=2t2 + t + 4 then find velocity at time 5 sec.​

Answer 1

Answer:

Hope it helps you.....

Answer 2

Question:

If the displacement, s = 2t² + t + 4 then find velocity ,v at time 5 sec.

Answer:

21 m/sec

Note:

• Displacement is the shortest path between the initial and final position.

• Velocity is the displacement per unit time.

• Acceleration is change in velocity per unit time.

• If we have the displacement as a function of time, say s(t) ,then the velocity is given by ;

v(t) = ds(t)/dt .

Also,

The instantaneous velocity at t = k , is given as v(k) .

• Also, the acceleration is given by ;

a(t) = dv(t)/dt .

Also,

The instantaneous acceleration at t = k , is given as ; a(k)

• d(t^n)/dt = n•t^(n-1)

• d(constant)/dt = 0

Solution:

Here,

The displacement as a function of time is ;

s(t) = 2t² + t + 4

Thus,

=> v(t) = ds(t)/dt

=> v(t) = d(2t² + t + 4)/dt

=> v(t) = d(2t²)/dt + dt/dt + d(4)/dt

=> v(t) = 2•dt²/dt + dt/dt + d(4)/dt

=> v(t) = 2•2•t^(2-1) + 1 + 0

=> v(t) = 4t + 1

Now,

The instantaneous velocity at t = 5 sec , will be ;

=> v(t) = 4t + 1

=> v(5) = 4•5 + 1

=> v(5) = 20 + 1

=> v(5) = 21

Hence,

The instantaneous velocity at t = 5 sec will be ;

21 m/sec