Question

The position y of a particle is varying with time tas y =
a + bt + cť + dt4. The initial rate of change of position
of the particle is.​

Answer 1

Answer:

Displacement as function of time is given.

y=a+ bt+ ct^2 + dt^4…………….(1)

The time derivative of displacement or time rate of change of displacement gives velocity. Therefore, differentiating equation (1) w r t time, we get,

velocity,v=dy/dt=b + 2ct +4dt^3…………..(2)

To find velocity at t=0, we put t=0 in equation (2). Then,

v( at t = 0)= b……………..(3)

The time derivative of velocity gives acceleration. Therefore, differentiating equation (2) wrt time, we get,

dv/dt = a( acceleration)= 2c + 12 dt^2………