The velocity of a particle follows the following function v(t)=2t^2-1 in the unit of m/s. Find the acceleration of the particle at t=1s? O A. 3 m/s^2 O B. 1 m/s^2 O C. 2 m/s^2 O D. 4 m/s^2
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
We know that acceleration of a particle is rate of change of velocity with respect to time.
Acceleration (a) =( dV/dt ) i.e differentiation of Velocity V(t) with respect to time.
Differentiation of t^n is n× t^(n-1) i.e
(dt^n / dt ) = (n× t^n-1 )
Differentiation of a constant is zero. I.e (d(K)/dt ) = 0
Differentiation of two function in sum can be written as :-
d(u+v) /dt =( du/dt) + (dv/dt)
If a constant is multiplied then it comes out from the differentiation operator (d/dt)
d(kt^n )/dt = k( dt^n/dt).
Above formula is going to be used in the solution.
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