Question

Displacement of a particle is given by x= 3t2+2t. Determine the instantaneous velocity. Also find instantaneous acceleration.

Answer 1

Answer:

For Instantaneous velocity differentiate the displacemrnt equation wrt t

i.e., v= 6t+2

For Instantaneous accelration differentiate the velocity equation wrt t

i.e., a= 6 m/s^2

Answer 2

Answer :

Displacement = x = 3t² + 2t.

Differentiating x :

⇒ v = dx/dt

⇒ 3*2t + 2

⇒ 6t + 2 m/s

Hence, Instantaneous velocity = (6t + 2) m/s.

Now, Instantaneous velocity at 1 seconds :

⇒ 6*1 + 2

⇒ 6 + 2

⇒ 8 m/s

Hence, Instantaneous velocity at t = 1 seconds : 8 m/s.

Now, Instantaneous acceleration :

Differentiating v :

⇒ 6 + 0

⇒ 6 m/s²

Hence, Instantaneous acceleration = 6 m/s².

Some Additional Information -

• Distance is a scalar quantity and displacement is a vector quantity.

• Speed is a scalar quantity and velocity is a vector quantity.

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

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

• Speed is defined as the distance travelled per unit time.

• Velocity is displacement per unit time.