Question

the displacement of the particle moving along x axis is given by X=3t^3-5t^2+1 where x is in meter & the it is in second. calculate instantaneous velocity at, t=2 second

Answer 1

V = dx/dt
V = d(3t³-5t²+1)/dt
V = 3×3t²-5×2t+0
V = 9t² -10t

Therefore instantaneous velocity at 2 s is
V = 9t² -10t
V = 9(2)²-10(2)
V = 36-20
V = 16 m/s

Answer 2

Answer :

Displacement = x = 3t³ - 5t² + 1.

Differentiating x :

⇒ v = dx/dt

⇒ 3*3t² - 2*5t + 0

⇒ 9t² - 10t

Now, Instantaneous velocity at 2 seconds :

⇒ 9*2² - 10*2

⇒ 9*4 - 20

⇒ 36 - 20

⇒ 16 m/s

Hence, Instantaneous velocity at time of 2 seconds = 16 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.