Question

Discuss the motion of the particle in every interval(whether it is slowing down or speeding up) [By using slope for acceleration]​

Answer 1

Given:

We have been provided with velocity - time graph of an object.

To Discuss :

Type of motion of the particle in various phases of journey using slope method

Concept:

We should remember that the slope of Velocity vs Time graph gives us the acceleration of the particle

$\boxed{Acc. = \dfrac{\Delta v}{\Delta t}}$

Calculation:

1. In the part O - A :

$acc. = slope = \dfrac{10 - 0}{2 - 0} = 5 \: m {s}^{ - 2}$

So particle is following Accelerated Motion (constant Acceleration)

2. In the part A - B :

$acc. = slope = \dfrac{10 - 10}{6 - 2} = 0 \: m {s}^{ - 2}$

So particle is Following uniform motion with constant velocity

3. In the part B - C :

$acc. = slope = \dfrac{0 - 10}{8 - 6} = - 5 \: m {s}^{ - 2}$

So the particle is again following Negatively Accelerated motion such that it's velocity is reducing .

4. In the part C - D :

$acc. = slope = \dfrac{ - 10 - 0}{10 - 8 } = - 5 \: m {s}^{ - 2}$

It is still Following retarded motion with same magnitude of acceleration such that the velocity of the particle has changed its direction.

The particle is moving in opposite direction now.

5. In the part D - E :

$acc. = slope = \dfrac{ 0 - ( - 10)}{10 - 8 } = + 5 \: m {s}^{ - 2}$

So the particle is experiencing accelerated Motion in a direction opposite to the previous part .

Finally the velocity became zero .

Answer 2

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