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.
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb73f2c50-3d74-44b8-bc0a-ed754c304ddd%2F9eef3597-9d85-48d4-842c-4b795bce0927%2F8japd2_processed.png&w=3840&q=75)
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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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