Question

the displacement of a particle(in m) moving along x axis is given by x=78t2 +12t. calculate the instantaneous velocity at 2s, avg velocity between 2s and 3s, instantaneous acceleration

Answer 1

Answer:

Displacement of the particle = x = 78t² + 12t.

Differentiating :

⇒ v = dx/dt

⇒ 2*78t + 12

⇒ 156t + 12.

Now, Finding velocity at 2 sec = 156*2 + 12 = 312 + 12 = 324 m/s.

Hence, instantaneous velocity at time 2 seconds = 324 m/s.

Now, Finding velocity at 3 sec = 156*3 + 12 = 468 + 12 = 480 m/s.

Average velocity = (v - u)/(t2 - t1) = (480 - 324)/(3 - 2) = 156/1 = 156 m/s.

Hence, Average Velocity between 2s and 3s = 156 m/s.

Differentiating :

⇒ a = dv/dt

⇒ 156 + 0

⇒ 156 m/s²

Hence, Instantaneous acceleration = 156 m/s².