Question

Displacement equation of a particle moving along x- axis is given by S = 8 + 3 t + 4 t² . Find the velocity of particle at t = 5 s and instantaneous acceleration.

Answer 1

Answer:

X = 4t ²+ 3t + 7

V =

dt

dx

= instantaneous velocity

V = 8t + 3

at t = 2

v = 19 m/s

a =

dt

dv

instantaneous accelesation

a= 8 (constant)

at t = 2

a=8 m/s

2

Answer 2

Answer :

Displacement = x = 8 + 3t + 4t².

Differentiating x :

⇒ v = dx/dt

⇒ 0 + 3 + 2*4t

⇒ 3 + 8t

Now, Instantaneous velocity at 5 seconds :

⇒ 3 + 8*5

⇒ 3 + 40

⇒ 43 m/s

Hence, Instantaneous velocity at time of 5 seconds = 43 m/s.

Now, Instantaneous acceleration :

Differentiating v :

⇒ a = dv/dt

⇒ 0 + 8

⇒ 8 m/s²

Hence, Instantaneous acceleration = 8 m/s².