Question

The velocity-time graph of a body is shown in graph of a body is shown in fig. The displacement covered by the body in
8s is​

Answer 1

Answer:

Given:

Velocity time graph has been provided in the attachment.

To find:

Displacement of the body in 8 seconds.

Concept:

Displacement is the shortest distance between starting and stopping point .

In other words , it is given by the area enclosed within the velocity time graph.

Areas under the curve can be easily found out with our knowledge of area of triangle, trapezium and square.

Calculation:

Total displacement

= sum of areas of individual parts

= (2 × 1) + { ½(2 + 6) × 1} + (½ × 1 × 6) -

{½ × (2 + 1) × 6 } + (2 × 4)

= 2 + 4 + 3 - 9 + 8

= 8 metres.

Final answer : Displacement is

8 metres.

Note that:

Areas below the x axis have been considered to be negative because displacement is a vector.

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

We have to see the X-Axis (which is time) and Y-axis which is velocity.

So, we know that :

$\star {\boxed{\sf{Velocity \: = \: \dfrac{Displacement}{Time}}}}$

And

★ Displacement = Time * Velocity

We have to find displacement using the given graph in 8 seconds.

We need to find all the parts separately :

Calculations :

(2 * 1) + [½ (2 + 4) * 1] + [½ * 1 * 6] - [½ ( 2 + 1) * 6] + (½ * 1 *6) + 2(4)

⇒2 + ½(6) + ½(6) - ½(3)*6 + 8

⇒2 + 3 + 3 - ½*18 + 8

⇒2 + 6 - 9 + 8

⇒2 - 3 + 8

⇒8 - 1

⇒7 cm

∴ Displacement = 7 cm