Kinematics of Motion Introduction - The relative motion of bodies without consideration of the forces causing the motion. - kinematics deal with the geometry of motion and concepts like displacement, velocity and acceleration considered as functions of time ● When the motion of a body is confined to only one plane, the motion is said to be plane motion ● Rectilinear Motion-is the simplest type of motion and is along a straight line path. ● Curvilinear Motion-It is the motion along a curved path. Such a motion, when confined to one plane, is called plane curvilinear motion. ● Linear Displacement; It may be defined as the distance moved by a body with respect to a certain fixed point. The displacement may be along a straight or a curved path. ● Linear Velocity ; It may be defined as the rate of change of linear displacement of a body with respect to the time.
v = ds/dt
Linear Acceleration; It may be defined as the rate of change of linear
velocity of a body with respect to the time.
or Equations Of Linear Motions Graphical Representation of Displacement with Respect to Time Graphical Representation of Velocity with Respect to Time 1. When the body moves with uniform velocity: We know that distance covered by a body in time t second
= Area under the v-t curve AB
= Area of rectangle OABC
Thus, the distance covered by a body at any interval of time is given by the area under the v-t curve.
2. When the body moves with variable velocity
v = u + a.t, and s = u.t + 1/2a.t^2 may be verified from this v-t curve. Graphical Representation of Acceleration with Respect to Time
1.When the body moves with uniform acceleration;
Since the change in velocity is the product of the acceleration and the time, therefore the area under the a-t curve (i.e. OABC) represents the change in velocity. 2. When the body moves with variable acceleration;
Let at any instant of time t, the acceleration of moving body is a.
Mathematically;
Integrating both sides,
where v1 and v2 are the velocities of the moving body at time intervals t1 and t2 respectively.
the above expression may be written as;
Worked Examples 1. A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. Calculate the acceleration and the time taken to attain the speed. If a further acceleration raises the speed to 90 km. p.h. in 10 seconds, find this acceleration and the further distance moved. The brakes are now applied to bring the car to rest under uniform retardation in 5 seconds. Find the distance travelled during braking. 2.The motion of a particle is given by , where a is the acceleration in m/s2 and t is the time in seconds. The velocity of the particle at t = 1 second is 6.25 m/s, and the displacement is 8.30 metres. Calculate the displacement and the velocity at t = 2 seconds.
