Question

Is a 13 year old boy willing 2 date a 13 year old girl? answer yes and send a friend request. Please say yes!

Answer 1

Answer:

Uniform acceleration: When the change in the velocity of a moving body is the same in each second then its acceleration is said to be uniform. Such motion is said to be uniformly accelerated motion or uniform motion.

Non-Uniform acceleration: When the change in velocity of a moving body is not the same in each second then its acceleration is said to be non-uniform acceleration. Such motion is called non-uniform motion.

The equation of motions from the velocity-time graph:

The velocity-time graph for a body under uniform acceleration is shown in the figure.

Let initial velocity of the body = u

The final velocity of the body = v

Time is taken by the body = t

Acceleration of the body = a

Derivation of the first equation of motion:

According to the definition,

Acceleration of a body = Rate of change of velocity i.e. slope of the velocity-time graph.

The velocity-time graph for a uniformly accelerated body is given by the straight line AB. So, acceleration of the body is equal to the slope of the line AB.

Acceleration = Slope of line AB =ADBD=ADBC−DC

From the velocity time graph,

BC=v,DC=OA=u,AD=OC=t

Then, a⇒tv−u⇒at=v−u⇒v=u+at

⇒ First equation of motion

Derivation of the second equation of motion

Under the uniform acceleration, from the figure, one can write

Distance travelled (s) = Area of trapezium OABC

S = Area of the triangle ABD + Area of rectangle OADC

 =21×AD×BD+OC×OA

Here, AD=OC=t

and BD=BC−DC=v−u

BD=u+at−u=at and OA=u

∴s=21×t×at+t×u⇒s=ut+21at2

This is second equation of motion.

Derivation of third equation of motion

Distance travelled, s = Area of the trapezium OABC