Question

Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure.Work done by all the forces on the particle is
1) 400 J
2) – 400 J
3) – 200 J
4)200J
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Answer 1

Answer:

-400J

Explanation:

Hey.

As by the graph the final velocity becomes zero

$workdone = chage \: in \: kinetic \: enrgy$

$initial \: velocity = 20m {s}^{ - 1} (by \: graph) \\ final \: velocity = 0 \\ \\ workdone = 0 - \frac{1}{2} \times m \times v {}^{2} \\ = - \frac{1}{2} \times 2 \times 20 \times 20 \\ = - 400joule$

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Answer 2

Answer:

W=400j

Hint: The velocity-time graph shows the value of velocity along the y-axis with respect to time along the x-axis. Find the acceleration from the given velocity and time.

The force is the product of the mass of the object and the acceleration.

The amount of the work-done is gained by the product of the force and the displacement.

Note that, we can find the displacement by calculating the area covered by the figure in the velocity-time graph.

Formula used:

Acceleration a=v(velocity)t(time)

Now the applied force can be written as F=m×a , here m is known as the mass of the object

The work-done W=F×s

s= the displacement = the area of the triangle that covers the velocity-time graph

=12×base×height

=12vt

Complete step by step answer:

The above graph is a velocity-time graph where the velocity is along the y-axis and the time is along the x-axis.

Given that, the velocity, v=20m/s at time t=2sec

So the Acceleration

a=v(velocity)t(time)

a=202=10m/s2

The mass of the object m=2kg

The applied force F=m×a=2×10=20N

We know the work done is defined by the product of the applied force on an object and the displacement of that object due to this force.

Hence, The work-done W=F×s

Now the displacement is calculated by measuring the area of the triangle shown in the graph.

s=12×base×height

⇒s=12×2×20

s=20m

So, The work-done W=F×s=20×20

⇒W=400J

So the work-done by the forces acting on the object is W=400J