Question

derive an equation of motion v=vo+at using v-t graph

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Answer 1

Answer:

Concept :

Equations of motion connect an object's displacement to its speed, acceleration, and time. An object's motion can take a variety of different routes. Here, we'll concentrate on linear motion. When measuring displacement, velocity, and acceleration, we employ both positive and negative numbers, with negative values pointing in the opposite direction of positive values. The equation s=vt, where s,s is the displacement, v,v is the velocity, and t,t is the time over which the motion happened, is what we have if there is no acceleration. The more general formulae for constant acceleration below are essentially a specific example of this.

Explanation:

• U is the velocity at time t1, and V is the velocity at time t2. The rate of change in velocity is known as acceleration if it is shown as a symbol. The first linear motion equation is this one.
• Consider an object travelling in a straight line with uniform acceleration.
• Let u represent the object's beginning velocity at time t=0 and v represent the item's end velocity at time t.
• Let s represent the distance the object travelled in time t.

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Answer 2

Answer:

Graph plotted with time on x−axis and velocity on y axis is called V−t graph. V−t graph of a particle having constant acceleration a distance travelled by particle is area under (V−t) graph.

Explanation:

For the derivation, let us consider a body moving in a straight line with uniform acceleration. Then, let the initial velocity be u, acceleration is denoted as a, the time period is denoted as t, velocity is denoted as v, and the distance travelled is denoted as s.

Derivation of First Equation of Motion by Graphical Method

The first equation of motion can be derived using a velocity-time graph for a moving ob

In the above graph,

The velocity of the body changes from A to B in time t at a uniform rate.

BC is the final velocity and OC is the total time t.

A perpendicular is drawn from B to OC, a parallel line is drawn from A to D, and another perpendicular is drawn from B to OE (represented by dotted lines).

The following details are obtained from the graph above:

The initial velocity of the body, u = OA

The final velocity of the body, v = BC

From the graph, we know that

BC = BD + DC

Therefore, v = BD + DC

v = BD + OA (since DC = OA)

Finally,

v = BD + u (since OA = u) (Equation 1)

Now, since the slope of a velocity-time graph is equal to acceleration a.

So,

a = slope of line AB

a = BD/AD

Since AD = AC = t, the above equation becomes:

BD = at (Equation 2)

Now, combining Equation 1 & 2, the following is obtained:

v = u + at