One dimension

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 =


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)