Question

Represent the following graphically:
a. An object at rest
b. An object moving with uniform speed
c. An object moving with non-uniform speed

Answer 1

Answer:

• didn't move
• an object is in uniform motion if it travels equal distance in equal interval of time

Answer 2

Answer:

a. An object at rest.

b. An object moving with uniform speed.

c. An object moving with non-uniform speed.

All three graphs are attached in the picture.

Explanation:

a) An object at rest:

The object is at any point suppose $b$, at rest.

The equation of this condition:

$x=b$

where, $x=$ distance travelled and $b=$ any point

The graph for an object at rest is shown in the picture.

b) An object moving with uniform speed:

$velocity=Constant\\ \begin{aligned}&v=c \\&\frac{d x}{d t}=c \\&\int d x=\int c \cdot d t \\&x=c t+b\end{aligned}$

where, $x=$ distance travelled, $t=$ time and $c,b=$ Constant

The graph for an object moving with a uniform speed is shown in the picture.

c) An object moving with non-uniform speed:

$Acceleration=Constant$

$\begin{aligned}a &=c \\\frac{d v}{d t} &=c \\\int d v &=\int c \cdot d t \\v &=c t \\\frac{d x}{d t} &=c t \\\Rightarrow & \int d x=\int c t \cdot d t \\\Rightarrow & x=c t^{2}+c'\end{aligned}$

where, $x=$ distance travelled, $t=$ time and $c,c'=$ Constant

The graph for an object moving with non-uniform speed is shown in the picture.