Motion on straight line
•Distance-Actual distance travelled by body. (scalar)
•Displacement-Shortest distance travelled between two points. (vector)
•“Distance can't be zero but displacement may be zero.”
•Distance ≥Displacement
•Speed-It’s the rate of change of distance.(scalar)
•Velocity-It’s the rate of change of displacement.(vector)
Instantaneous and average velocity
•Instantaneous speed/velocity-It is the speed/velocity at a exact point of motion.
Instantaneous speed/velocity=or
•Average speed/velocity-It is the average of speed/velocity on motion of particle on large interval of time.
Average speed/velocity =
Methodologies
i. When a body covers a distances at constant velocities then,
=
so, =
If (covers equal distances)
(H.M. between velocities)
ii.When a body travels with V1, V2, V3,....... Vn for equal interval of time.
==
=
for t1 = t2 = t3 =....... = tn ( in equal time) then,
(A.M. between velocities)
Equations of motion (air resistance is neglected)
If x=displacement, v=velocity, a=acceleration, t=time taken then
( for instantaneous , )..........(i)
(for instantaneous, )............(ii)
If v=final velocity, u=initial velocity, s=distance travelled, t=time taken, a=constant acceleration then
i. {From (ii), }...........(iii)
ii.{From (i) and (ii), }
iii. {From (i) from(ii) so }
iv. The distance travelled on successive second =
If air resistance is not neglected time of descent>time of ascent.
Graph of equations of motion
If d=distance, t=time, v=velocity, a=acceleration.
(1) Slope of d-t graph gives avg. velocity.(Intercept on y axis gives initial displacement)
(2) Slope of v-t graph gives avg. acceleration.
(Intercept on y axis gives initial velocity)
(3) Area of v-t graph gives distance covered.
(4) Area of a-t graph gives change in velocity.
(Intercept gives in initial acceleration)