Question

The position coordinate of a moving particle is given by x=6+18t+9t^2. calculate the instantaneous speed of the particle at t=2s. ​

Answer 1

Answer:

x=6+18(2)+9(4)

=6+36+36

=42+36

=78

Answer 2

Answer :

Displacement = x = 6 + 18t + 9t².

Differentiating x :

⇒ v = dx/dt

⇒ 0 + 18 + 2*9t

⇒ 18 + 18t

Now, Instantaneous velocity at 2 seconds :

⇒ 18 + 18*2

⇒ 18 + 36

⇒ 54 m/s

Hence, Instantaneous velocity at time of 2 seconds = 54 m/s.

Some Additional Information -

• Speed is the distance travelled per unit time.

• Velocity is the displacement per unit time.

• Speed is a scalar quantity.

• Velocity is a vector quantity.

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

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