Question

The displacement (m) of a particle moving along x-axis is given by x = 18t+5t^2 .Calculate the (i) instantaneous velocity at t= 2s .(ii)average velocity at t= 2s and 3s.(iii) instantaneous acceleration

Answer 1

The answer is in the image

Sorry for messy presentation..

Answer 2

Answer :

Displacement = x = 18t + 5t².

Differentiating x :

⇒ v = dx/dt

⇒ 18 + 2*5t

⇒ 18 + 10t

Now, Instantaneous velocity at 2 seconds :

⇒ 18 + 10*2

⇒ 18 + 20

⇒ 38 m/s

Hence, Instantaneous velocity at time of 2 seconds = 38 m/s.

Now, Instantaneous velocity at 3 seconds :

⇒ 18 + 10*3

⇒ 18 + 30

⇒ 48 m/s

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

⇒ (48 - 38)/(3 - 2)

⇒ 10/1

⇒ 10 m/s

Hence, The Average Velocity between t = 2s and t = 3s is : 10 m/s.

Now, Differentiating v :

⇒ a = dv/dt

⇒ 0 + 10

⇒ 10 m/s²

Hence, The Instantaneous acceleration is : 10 m/s².