A particle moves along a straight line with a constant acceleration

PHYSICS · Multi-part · CBSE · Physics · Motion in a Straight Line · Motion in a Straight Line

Problem

a

. On integrating the definition of acceleration, an expression for its velocity and then for its displacement as a function of time are obtained. (i) Starting from

a=\dfrac{dv}{dt}

, write the integrated expression for the velocity

v

in terms of the integration constant

C_1

. (ii) Explain the physical meaning of the constant

C_1

and state how its numerical value is fixed for an actual motion. (iii) The velocity obtained in part (i) is substituted in

v=\dfrac{dx}{dt}

and integrated once again to give the displacement

x

in the form

x=C_2+u t+\dfrac12 a t^{2}

. Explain the physical meaning of the second constant of integration

C_2

and describe the usual choice made for it in derivations of kinematic equations.

Related theory

Kinematic Equations for Uniform Acceleration
Calculus for motion
Kinematic equations for uniformly accelerated motion
Motion in a Straight Line

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