Question

motion of the particles describe by x=a+bt^2 when a= 15 cm and b=3cm find instantaneous velocity at time 3 sec?

Answer 1

On taking the derivative of the equation, you get
v = 2bt
As a is not present in the mentioned equation, we take only b=3cm, and t=3s. Then,
v = 2×3×3
= 18 m/s

Answer 2

Answer:

The instantaneous velocity at time 3 sec is 18 m/s.

Explanation:

Given that,

a = 15 cm

b = 3 cm

time t = 3 sec

Motion of the particle is

$x=a+bt^2$

Velocity :

The velocity is the rate of change of the position of the particle.

$v = \dfrac{dx}{dt}$

The position of the particle is,

$x=a+bt^2$

On differentiating w.r.to t

$v= \dfrac{dx}{dt}=2bt$

The velocity at t= 3,

$v = 2\times3\times3$

$v =18\ m/s$

Hence, The instantaneous velocity at time 3 sec is 18 m/s.