Question

Displacement of a particle x=5t²+2t m calculate instantaneous velocity and instantaneous acceleration in time t=4s​

Answer 1

Explanation:

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Answer 2

Answer :

Displacement = x = 5t² + 2t.

Differentiating x :

⇒ v = dx/dt

⇒ 5*2t + 2

⇒ 10t + 2

Now, Instantaneous velocity at 4 seconds :

⇒ 10*4 + 2

⇒ 40 + 2

⇒ 42 m/s

Hence, Instantaneous velocity at time of 4 seconds = 42 m/s.

Now, Instantaneous acceleration :

Differentiating v :

⇒ 10 + 0

⇒ 10 m/s²

Hence, Instantaneous acceleration = 10 m/s².

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.

• The magnitude of displacement is equal to or less than the magnitude of distance.

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

• Speed is the Distance travelled per unit time.

• Velocity is the Displacement per unit time.

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