Question

From velocity-time graph we can find
the displacement of the body.
acceleration of the body.
displacement velocity and acceleration of the body
none of these.​

Answer 1

(i) Acceleration of a body

(ii) the displacement of a body and

(iii) the distance traveled in a given time

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ANSWER

The Velocity-Time graph gives the change of velocity with the change in time

Y-Axis: Velocity

X-Axis: Time

Now, the slope of the velocity-time graph is given as

Slope=

Δx

Δy

=

Δt

Δv

Since, y=v (Velocity)

And x=t (time)

Now, there are three types of Velocity-Time graph

(a) Velocity is constant-Uniform Motion

this means that velocity remains the same for all time

(b) Uniformly Accelerated Motion

This means that velocity changes at a constant rate

Slope = Constant and the graph is a straight-line graph

(c) Non-Uniformly Accelerated Motion

This means that velocity changes at a variable rate

Slope = Variable and the graph is as shown

Velocity-Time graph can be used to find the following as:

(a) Acceleration:

The slope of Velocity − Time Graph=Acceleration

Since Slope=

Δt

Δv

So, Acceleration

Δt

Δv

And hence, Slope = Acceleration

(b) Displacement of a body

The area under the velocity − Time graph gives the displacement of the body

Displacement = Velocity × Time

The area under the graph = Displacement of body

For finding the area, we multiply the velocity and time

(c) The distance of body:

Distance = Speed × Time

Now, Speed its magnitude of the velocity

Hence as long as the velocity is positive,

The area under the curve = Distance

NOTE:

If velocity is negative, then the area under the curve is negative and then the total area gives the displacement. So, in that case

Distance



= Displacement

Example: Let the velocity-time graph be as shown below:

Now Displacment= Area under the curve

=

2

1

×5×2−

2

1

×5×2+

2

1

×5×2=5m

Whereas Distance =

2

1

×5×2+

2

1

×5×2+

2

1

×5×2=15m

For displacement, we have considered the area below the time axis as negative whereas, for distance, we have considered all areas as positive like this answer plz follow me