Using differentiation in kinematics?

Great question JuJu.

The derivative of the acceleration is called the 'jerk', or sometimes 'jolt'.

This concept is very important to engineers, especially when designing theme park attractions like a roller coaster.

Passengers of the roller coaster can only take a jerk below a certain value, otherwise they will probably suffer whiplash.

Of course, when the acceleration is constant, the jerk is zero.

The derivative of the 'jerk' is called the 'jounce', aka the 'snap'. I'm not sure if it has any practical significance.

There is no official name for the derivative of the 'snap', however, somewhat amusingly, it has been referred to as the 'Crackle' or 'Pop'

no not really sadly. if you have constant acceleration then differentiating the acceleration equation will give you an answer of 0

S=T^3-7T^2+10T T>0 a) discover the values of t (t>0) at which P passes with the aid of O. whilst P passes with the aid of O S = 0 0=T(T - 2)(T - 5) P passes with the aid of O at 0, 2 and 5 seconds --------------------------------------... b) discover the linked fee of P each and every time it passes with the aid of O. S=T^3-7T^2+10T speed = dS/dT = 3T^2 - 14T + 10 whilst T = 0, speed = 10 m/sec whilst T = 2, speed = -6 m/sec whilst T = 5, speed = + 5 m/sec --------------------------------------... c) discover the main suitable speed of P interior the era 0<T<5 At Max or Min dS/dT= 0

no it doesn't