Question

Establish the relation x=vt+1/2 at^2 by graphical method.

Answer 1

Answer:

x = ut+1/2at^2

Explanation:

• In a velocity-time graph, the area under the graph is the magnitude of the displacement
• Consider an object with initial velocity = u, final velocity = v, time of motion = t, acceleration = a and the displacement = x
• To find the area under the graph, we need to add the areas of the rectangle AODC and the area of the triangle ABD
• Area of rectangle AODC = AO*OC = ut
• Area of triangle ABD = 1/2*AD*BD = 1/2 t (v-u)
• We know that v = u +at
• so v-u = at
• BD = v-u = at
• Area of triangle ABD = 1/2*AD*BD = 1/2 t (at) = 1/2at^2
• The total area under the graph = AODC + ABD = ut + 1/2at^2
• displacement = ut + 1/2at^2
• x = ut + 1/2at^2

This is the proof for x = ut + 1/2at^2.

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Answer 2

Answer:

The answer is x = ut+1/2at^2

Explanation:

In a velocity-time graph, the area under the graph is the magnitude of the displacement

Consider an object with initial velocity = u, final velocity = v, time of motion = t, acceleration = a and the displacement = x

To find the area under the graph, we need to add the areas of the rectangle AODC and the area of the triangle ABD

Area of rectangle AODC = AO*OC = ut

Area of triangle ABD = 1/2*AD*BD = 1/2 t (v-u)

We know that v = u +at

so v-u = at

BD = v-u = at

Area of triangle ABD = 1/2*AD*BD = 1/2 t (at) = 1/2at^2

The total area under the graph = AODC + ABD = ut + 1/2at^2

displacement = ut + 1/2at^2

x = ut + 1/2at^2

This is the proof for x = ut + 1/2at^2.

motion of an item.

to narrate the slope price of the line on a pace-time graph at a given time or throughout a given time frame to the immediately or the common speed of an item and to decide such speed values the usage of a slope calculation.

to narrate the vicinity among the line and the time-axis of a pace-time graph to the displacement of the item and to decide such displacement values the usage of a place calculation.

to relate the movement of an item as defined through a velocity-time graph to other representations of an object's movement - dot diagrams, movement diagrams, tabular facts, and so forth.

to investigate role-time graphs and transpose them into the corresponding speed-time graphs (and vice versa).

the rate is regular (c) throughout the time interval. No particles of matter how a good deal the time adjustments, the rate can be c at every instantaneous. In this situation, we have taken the preliminary speed to be high quality. The graph could be exclusive if the preliminary velocity is terrible.

instance: If the acceleration of a particle is 0 (0), and velocity is continuously said 5 m/s at t =zero, then it'll stay regular throughout the time.

Establish the relation x=vt+1/2 at^2 by graphical method.

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