Question

The displacement in metre of a particle moving along x-axis is given by x=4t^2_15t+25 calculate the instantaneous velocity at t=2 ,average velocity between t=2s and t=3s and instantaneous acceleration

Answer 1

Explanation:

by differentiation V=8t-15,now at t=2sec instantaneous velocity is 8*2+15=31m/s.

Answer 2

Answer :

Displacement = x = 4t² - 15t + 25.

Differentiating x :

⇒ v = dx/dt

⇒ 2*4t - 15 + 0

⇒ 8t - 15

Now, Instantaneous velocity at 2 seconds :

⇒ 8*2 - 15

⇒ 16 - 15

⇒ 1 m/s

Hence, Instantaneous velocity at time of 2 seconds = 1 m/s.

Now, Instantaneous velocity at 3 seconds :

⇒ 8*3 - 15

⇒ 24 - 15

⇒ 9 m/s

Now, Average velocity = (v2 - v1)/(t2 - t1)

⇒ (9 - 1)/(3 - 2)

⇒ 8/1

⇒ 8 m/s

Hence, The Average Velocity between t = 2s and t = 3s is : 8 m/s.

Now, Differentiating v :

⇒ a = dv/dt

⇒ 8 - 0

⇒ 8 m/s²

Hence, The Instantaneous acceleration is : 8 m/s².