Derive the following equations for uniformly accelerated motion by graphical method. a) Velocity -time relation b) Position - time relation 3) Position – velocity relation.

Skip to content# Derive the following equations for uniformly accelerated motion by graphical method. a) Velocity -time

##
This Post Has 10 Comments

### Leave a Reply

Derive the following equations for uniformly accelerated motion by graphical method. a) Velocity -time relation b) Position - time relation 3) Position – velocity relation.

a) velocity - time realation

that graph's gradient gives the uniform acceleration

Conclusion E

Explanation:

In this study we need to keep several things is mind.

First, the atracttion between two objects can be calculated using Newton's Universal Gravitation Equation:

[tex]F = G * \frac{M_{1} * M_{2}}{r^{2} }[/tex]

Where the Force of attraction between two objects can be calculate by the product of the Gravitational Constant (G), their masses between the square of the distance. This same equation can be used to obtain the acceleration caused by gravity.

If we take in account this equation, we know that the Earth Mass is so big that any other will be attracted using the same force, no matter his size. Because of this, while the attraction between a Plastic Ball and a Rock should be different, the Earth's Mass makes irrelevant any weight like a little fluctuation.

Because of this, the Acceleration due Gravity should be constant between any object. A 70% bias is imposible. This made conclusions A, B and D Falses.

However the previous equation doesn't take in count the medium on which the two objects move. It is know that a object moving inside a fluid will experience friction which a force that oposses movemente and goes on the contrary direction, While the Plastic ball falls, the air around it will cause friction. This friction will always slow a falling object. Proving then, Conclusion C is false

In the case that a object falls, the air can provide resistant as proved before, however any irregularity on the surface of the ball can cause the ball to move and making the fall not truly straight, this can increase the time travel of the ball and slowing the ball fall. For this Conclusion E is the most likely to cause the error

The answer is D. The acceleration of the plastic balls is not uniform

Explanation:

The air resistance decreases the downward acceleration. Therefore, due to air resistance exist when the ball speed up, downward acceleration decreases. It makes that acceleration of the plastic ball not uniform. This is the reason why measured time is 35 % greater.

The acceleration of the plastic balls is not uniform.

Explanation:

A student is testing the kinematic equations for uniformly accelerated motion by measuring the time it takes for light weight plastic balls to fall to the floor from a height of 3 m in the lab. The student predicts the time to fall using g as 9.80 m/s2 but finds the measured time to be 35% greater. What is the most likely cause of the large percent error?

from the kinematic equation

s=ut+[tex]\frac{1}{2} *at^{2}[/tex]

s=3m

a=9.8m/s^2

t=?

substituting into the equation

3=0*t+0.5*9.8t^2

t^2=.6122

t=0.782secs

if it is found to be 35% greater , then it will be

1.35*0.782

1.056s

the only casue would have been that

the downward acceleration of the ball is not uniform

x₂ = x₁ + v₁t + at²/2

Explanation:

Right out of the textbook.

The most possible cause of 35% increase in time measured is due to the acceleration due to gravity which is 70% less than 9.80 m/s² at this location.

Explanation:

We know that for a linear motion

S=ut+(1/2)*a*t²

Where S= Distance covered

u= initial velocity

t=time period

a= acceleration due to gravity

Since the body is falling vertically downwards "a" is to be replaced by "g"

Moreover, The body is falling from rest "u"=0

Hence the equation reduces to S=1/2*g*t²

t²=2S/g

Since the "g" is in denominator thus a decreased value of "g" would mean increased period. Thus an increase of 35% in the period would translate to a 70% decrease in "g".

1. velocity time relation .

Let an object is moving with uniform acceleration.

u = initial velocity of object

v = final velocity of object

a = uniform acceleration

Let object reaches at point B after time (t) Now, from the graph

Slope = Acceleration (a)=

time

change in velocity

Change in velocity = AB = v - u

Time = AD = t

a=

t

v−u

Solving we get

v=u+at.........(1

st

equation of motion)

This means acceleration a is constant.

Let

a) vo be the initial speed, at t=0

b) v be the final speed after time t

c) d distance travelled in time t

Then we have:

a) v=vo+a×t

b) v²=vo²+2×a×d (Galilei's equation)

c) d=vo×t+a×t²/2

d) average speed vm=(vo+v)/2

Are you Indian Native?

b position-time relation