Question

(04) The figure shows the position-time (x-t)graph of
one-dimensional motion of a body of mass
0.8 kg. The magnitude of each impulse is​

Answer 1

As per the given figure of one-dimensional motion of s body of mass 0.8 kg, the magnitude of each impulse is 3.2 N-s

Therefore, Option (4) is correct.

Explanation:

The impulse acting on the body during the time interval of 2 seconds each is imparting a momentum to it.

Therefore, the Impulse = Change in Momentum

If we take anyone of the triangular region on the displacement time graph

Lets take the first triangular region

Since we know that rate of change of displacement is velocity

i.e. $v=\frac{dx}{dt}$

Therefore, the slope of the graph will give instantaneous velocity

Here the slope of the graph from 0 to 2 seconds and then from 2 to 4 seconds is constant

Therefore, the motion is uniform from 0 to 2 seconds and then from 2 to 4 seconds

Therefore the initial velocity from 0 to 2 seconds

$u=\frac{4-0}{2-0}$

$\implies u=\frac{4}{2}$

$\implies u=2$ m/s

The final velocity from 2 to 4 seconds

$v=\frac{0-4}{4-2}$

$\implies v=\frac{-4}{2}$

$\implies v=-2$ m/s

Initial momentum

$=mu$

$=0.8\times 2$ kg-m/s

$=1.6$ N-s

Final momentum

$=mu$

$=0.8\times (-2)$ kg-m/s

$=-1.6$ N-s

Change in momentum

=Final momentum - Initial Momentum

$=-1.6-1.6$

$=-3.2$ N-s

The magnitude of change in momentum $=3.2$ N-s

Therefore, the impulse imparted

= Magnitude of change in momentum

= 3.2 N-s

Hope this helps.

Know More:

Q: What is position time graph?

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Q: Study the speed time graph of a body given here and answer the following questions:

a) what type of motion is represented by OA?

b) what type of motion is represented by AB?

c)what type of motion is represented by BC?

d) find the acceleration of the body.

e) calculate the retardation of the body.

f) find out the distance travelled by the body from A and B.

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