Question

The displacement of an object is given by x = 14t2
+ 8t + 1 m. Find the instantaneous
velocity at t= 2s.

Answer 1

displacement is given by,
x=14t²+8t+1
differentiate with respect to t
dx/dt=28t+8
we know that:
instantaneous velocity ,v=dx/dt
when=2 second
dx/dt=28×2+8=56+8=64m/s

Answer 2

Answer :

Displacement = x = 14t² + 8t + 1.

Differentiating x :

⇒ v = dx/dt

⇒ 2*14t + 8 + 0

⇒ 28t + 8

Now, Instantaneous velocity at 2 seconds :

⇒ 28*2 + 8

⇒ 56 + 8

⇒ 64 m/s

Hence, Instantaneous velocity at time of 2 seconds = 64 m/s.

Some Additional Information -

• Distance is the length of the total path travelled by a body.

• Displacement is the shortest distance between the initial position and the final position of the body.

• Speed is the Distance travelled per unit time.

• Velocity is the Displacement per unit time.