Question

The displacement of a particle moving along x axis given by x=20t+10t^2.Calculate the instantaneous velocity at t=2s

Answer 1

Answer:

Explanation:

x(t) = 20t + 10t²

We know, differentiation of instantaneous displacement with respect to time gives instantaneous velocity

∴ differentiating both sides, we get,

dx(t)/dt = d(20t + 10t²)

⇒v(t) = (20 * 1 * t¹⁻¹) + (10 * 2 * t²⁻¹)

⇒v(t) = 20 + 20t

⇒v(2) = 20 + 20 * 2

⇒v(2) = 60 unit s⁻¹

Answer 2

Answer :

Displacement = x = 20t + 10t².

Differentiating x :

⇒ v = dx/dt

⇒ 20 + 2*10t

⇒ 20 + 20t

Now, Instantaneous velocity at time 2 seconds :

⇒ 20 + 20*2

⇒ 20 + 40

⇒ 60 m/s

Hence, Instantaneous velocity at time = 2 seconds is 60 m/s.

Some Additional Information -

• Distance is the length of 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.

• Speed is distance travelled per unit time.

• Velocity is displacement per unit time.