Question

If a particle is moving with velocity
y = 3t2 - 3t + 1
then find minimum possible velocity in
m/s :-​

Answer 1

Answer:

0.25 unit

Explanation:

The velocity time relation of a particle is given by

v = 3t² -3t + 1 , t≥ 0

To find the minimum possible velocity we need to compare local minimas and velocity at t = 0. Let us differentiate the fuction to find the points of local minima.

dv/dt = 6t - 3

Equating dv/dt = 0 gives t = 1/2.

To check if this is a point of minima or maxima we check the sign of d²v/dt².

d²v/dt² = 6 > 0

Hence t= 1/2 is a point of local minima. And local minimum velocity is

vᵐⁱⁿ = 3*(1/2)² - 3*(1/2) +1

= 3/4 - 3/2 + 1

= 1/4

= 0.25

At t = 0, v(0) = 3*0² - 3*0 + 1

= 1.

Now v(0) > vᵐⁱⁿ. Therefore vᵐⁱⁿ is the global minima. Hence minimum possible value of velocity is 0.25 unit.