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Motion Under Variable Acceleration

110.Find rela...

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110.Find relation between velocity (v) and position (x) if particle moving along x axis with acceleration a=Kx initially partial moving with speed u at t=0 and x=0

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Q. The initial velocity of a particle moving along

x -

u (a t t = 0 a n d x = 0)

and its acceleration a is given by

a = k x

. Which of the following equation is correct between its velocity

(v)

(x)

?

Q. A particle moves along x-axis with an initial speed

v_{0}

5 m s^{- 1}

. If its acceleration varies with time as shown in a-t graph in the figure.
a. Find the velocity of the particle at t = 4s.
b. Find the time when the particle starts moving along -x direction.

Q. A particle moves along the x-axis with acceleration a = 6(t- 1), where t is in seconds. If the particle is initially at the origin and moves along the positive x-axis with

v_{0}

= 2 m/s, analyze the motion of the particle.

Displacement-time equation of a particle moving along x-axis is

x = 20 + t^{3} - 12 t

(SI Units). Find, position and velocity of particle at time

t = 0

Q. For a body moving along

x -

axis, its velocity is given by

v = \frac{a}{b} (1 - e^{- b t})

a

b

are positive constant. At

t = 0, x = 0

x

of the particle with time

t

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