Question

X=2t+3t². Calculate instantaneous velocity at the=2s. X is displacement.

Answer 1

$x = 2t + 3 {t}^{2} \\ \frac{dx}{dt} = v = 2 + 6t \\ v(t = 2) = 2 + 6 \times 2 = 14$

Answer 2

Answer :

Displacement = x = 2t + 3t².

Differentiating x :

⇒ v = dx/dt

⇒ 2 + 3*2t

⇒ 2 + 6t

Now, Instantaneous velocity at 2 seconds :

⇒ 2 + 6*2

⇒ 2 + 12

⇒ 14 m/s

Hence, Instantaneous velocity at time of 2 seconds = 14 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.