Question

The posittion of a particle is given by x=4t^2.Find the instantaneous velocity when t=2s.Also find the average velocity between 0s and 3s

Answer 1

Answer:

x= 4t^2

v=dx/dt = 4*2t = 8t

At t= 2s,

v= 8t =8*2 = 16m/s

Similarly, at t= 0s

v0 = 8*0 = 0m/s

At t= 3s,

v3 = 8*3 = 24m/s

Average velocity between 0s and 3s =(0+24)/2 = 12m/s

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Answer 2

Displacement = x = 4t².

Differentiating x :

⇒ v = dx/dt

⇒ 2*4t

⇒ 8t

Now, Instantaneous velocity at 2 seconds :

⇒ 8*2

⇒ 16 m/s

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

Now, Instantaneous velocity at 3 seconds :

⇒ 8*3

⇒ 24 m/s

Now, Instantaneous velocity at 0 seconds :

⇒ 8*0

⇒ 0 m/s

Hence, Instantaneous velocity at time of 3 seconds = 24 m/s.

Average velocity = (v2 - V1)/(t2 - t1)

⇒ (24 - 0)/(3 - 0)

⇒ 24/3

⇒ 8 m/s

Hence, the average velocity between 0s and 3s is 8 m/s.