Question

the motion of a particle is describes of the equation x=a+bt2 where a=15cm and b=3cm/s2 . its instantaneous velocity at time 3s will be

Answer 1

x = a + bt²
x = 15 + 3t²
Differentiate with dt
v = 6t

At t = 3s
v = 6 × 3 = 18 cm/s

It’s instantaneous velocity at t = 3s is 18cm/s

Answer 2

x = a + bt^2

Plug in the values of a and b.

x = 15 + 3t^2

We know that x/t gives v

So differentiating the equation w.r.t t,
dx/dt = 2 x 3t = 6t

v = 6t

Now it's given that t = 3

So the instantaneous velocity will be 6 x 3 = 18m/s

Hope This Helps You!