Question

The position co-ordinate ‘r’ of a body is given r= at2 +bt+c. What is the value of velocity

Answer 1

Given info : The position co ordinate r of a body is given r = at² + bt + c.

We have to find the value of velocity at t₀

Solution : we know, velocity is the rate of change of displacement with respect to time. I.e., v = ∆x/∆t

If position of particle is variable, I mean if it is function of t , x(t) , then velocity is found by differenting x(t) with respect to time. I.e., v(t) = d{x(t)}/dt

Here r = at² + bt + c , it is clear that r is variable or function of time.

so, velocity of body , v(t) = d(at² + bt + c)/dt = 2at + b

At t = 0,

Velocity of body, u = 2a × 0 + b = b

At t = t₀

Velocity of body, v = 2at₀ + b