Question

The acceleration time (a-t) graph for a particle moving along x-axis is as shown in figure. The corresponding position-time (x-t)graph of the particle may be represented by​

Answer 1

Answer:

Given:

An Acceleration vs Time graph has been provided.

To find :

Corresponding Displacement vs Time graph.

Concept:

We can see that the acceleration first remains constant ( negative value) for sometime.

Then it changes to positive values and again becomes constant.

Let acceleration be "a", time be "t", velocity be "v" and displacement be "x"

For the 1st half of the motion , let us consider :

a = - k.........[ k => arbitrary constant]

=> dv/dt = - k

=> dv = (- k) dt

Integrating on both sides :

=> ∫dv = (-k) ∫dt

=> v = -kt

=> dx/dt = (-k) t

=> dx = (-k) tdt

Again integrating on both sides:

=> ∫dx = (-k) ∫tdt

=> x = (-k) t²/2

=> x = (-k/2) t²

So, x ∝ (-t²) .......( parabolic downwards)

So we are getting a downward parabola for the 1st half of the motion.

For the 2nd half of the motion, follow the same steps :

a = k

Then, v = kt and x = kt²

So, x ∝ (t²)........(upward parabola)

So we will get upward parabola for the 2nd half of the motion.

Hence Option 1) is correct.

Answer 2

Answer:

hi bbtrss to ibcs egg Thanksgiving