Kinematics of Particles Worksheet - 1

1.   The acceleration of a particle performing rectilinear motion is given by a = k.t m/s². It is found that v = -24 m/s  when t = 0 and v = 48 m/s when t = 4 sec. Also x = 0 at     t = 3 sec. Find the value of ‘k’ and also the position, velocity and acceleration of the particle at t = 2 sec.

2.   The acceleration of a particle performing rectilinear motion is given by a= -0.05 v² m/s² Knowing that v = 20 m/s at x = 0 find,

a) The position of the particle at v = 15 m/s  

b) The particle’s accelerations at x = 50 m.

3.   The motion of a particle moving in straight line is given by the expression                    s = t³ – 3t² + 2t + 5 where ‘s’ is the displacement in meters and ‘t’ is time in seconds. Determine

a)   Velocity and acceleration after 4 sec.

b)   Maximum or minimum velocity and corresponding displacement and

c)   time at which velocity is zero.

4.   The position of a particle moving along a straight line is defined by the relation            x = t³ – 9t² + 15t + 18 where x is expressed in meters and t in seconds. Determine the time, position and acceleration of the particle when its velocity becomes zero.

5.   Acceleration of a particle is given by a = -kx^-3  m/s² . Knowing at x = 2 m, v = 0 and at x = 0.5 m, v = 3 m/s. Determine

a)   The value of ‘k’

b)   The particle’s velocity at x = 1m.

6.   The velocity relation of a rectilinear moving particle is defined as v = 4t² - 3t – 1 m/s. At t = 0, x = -4 m. Determine

a.    the time at which the particle reverses its sense of motion

At t = 3 sec.

a)   Acceleration

b)   position

c)   Displacement

d)   Distance travelled.

7.   A particle performing rectilinear motion has its acceleration given by a = (2 – 5 t) m/s².  At t = 4 sec its velocity is 15 m/s and t = 8 sec. its position is 60 m. Find at       t = 0, the particles position, velocity and acceleration. Also find the time when its velocity becomes zero.

8.   The acceleration of a vehicle at any instant is given by the expression a = ( ) m/s² If the vehicles starts from rest, find its velocity when its displacement is 125 m. Also find its displacement when its velocity is 10 m/s.

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