• For a body at rest

• As the slope is zero, so speed of the body is zero.

• For a body moving with uniform speed

• For accelerated motion.

• The slope of graph is increasing with time

• For decelerated (speeding down) motion.

• Slope of graph is decreasing with time

• When a body moving with a uniform velocity.

• The slope of AB indicates zero acceleration

• When a body starts from rest and moves with uniform acceleration.

• Greater is the slope of v-t graph, greater will be the acceleration

• When a body is moving with uniform acceleration and its initial velocity is not zero.

• When a body is moving with increasing acceleration.

• Slope increases with time.

• When a body is moving with decreasing acceleration.

• Slope decreases with time.

• When a body is moving with a uniform retardation and its initial velocity is not zero.

• As θ > 90°, graph has a negative slope.

• An object is said to be in motion when its position changes with time.

• We describe the location of an object by specifying a reference point. Motion is relative. The total path covered by an object is said to be the distance travelled by it.

• The shortest path/distance measured from the initial to the final position of an object is known as the displacement.

• **Uniform motion:** When an object covers equal distances in equal intervals of time, it is said to be in uniform motion.

• **Non-uniform motion:** Motions where objects cover unequal distances in equal intervals of time.

• **Speed:** The distance travelled by an object in unit time is referred to as speed. Its unit is m/s.

• **Average speed:** For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object by the total time taken.

• **Velocity:** Velocity is the speed of an object moving in definite direction. S.I. unit is m/s.

• **Acceleration:** Change in the velocity of an object per unit time.

• **Graphical representation of motions**

(i) Distance-time graph

For a distance-time graph time is taken on x-axis and distance is taken on y-axis.

OA = CD = u

OE = CB = v

OC = AD = t

BD = BC – DC (Change in velocity)

AD is parallel to OC.

∴ BC = BD + DC = BD + OA

∴ BC = v and OA = u

We get v = BD + u

∴ BD = v – u ...(1)

In velocity-time graph, slope gives acceleration.

Substituting (2) in (1) we get

BD = v – u

at = v – u

∴ v = u + at

(ii) Equation for position-time relation:

Let us assume,

s = distance travelled by the object

t = in time t

a = with uniform acceleration.

∴ Distance travelled by the object is given by area enclosed with OABC in the graph.

∴ s = OABC

= (area of rectangle OADC) + (area of DABD)

Substituting

OA = u, OC = AD = t and BD = at

We get

(iii) Equation for position-velocity relation:

s = distance travelled by the object

t = in time t

a = moving with uniform acceleration

s = area enclosed by trapezium OABC

Substitute value of ‘t’ in (1)

• **Uniform circular motion:** When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.