Question

From a adjacent figure, a displacement-time graph of a body in a straight line . Find the distance covered and the displacement of the body at the end of 12 seconds.

Kindly solve it with a proper explanation :)

No spams please !!​

Answer 1

ANSWER:

• Distance covered at the end of 12 seconds = 40 m.

• Displacement covered at the end of 12 seconds. = 0 m.

TO FIND:

• Distance covered at the end of 12 seconds.

• Displacement covered at the end of 12 seconds.

EXPLANATION:

Distance covered in 12 seconds:

From 0 - 2 seconds, distance travelled = 10 m

From 2 - 6 seconds, distance travelled = 0 m [ As the line is parallel to x axis(time) ]

From 6 - 8 seconds, distance travelled = 10 m

From 8 - 10 seconds, distance travelled = 10 m

From 10 - 12 seconds, distance travelled = 10 m

Total distance travelled = 10 + 0 + 10 + 10 + 10 = 40 m

Displacement covered in 12 seconds:

From 0 - 2 seconds, displacement covered = 10 m

From 2 - 6 seconds, displacement covered = 0 m [ As the line is parallel to x axis(time) ]

From 6 - 8 seconds, displacement covered = - 10 m[ As the displacement decreases ]

From 8 - 10 seconds, displacement covered = - 10 m[ As negative displacement increases ]

From 10 - 12 seconds, displacement covered = 10 m[ As negative displacement decreases ]

Total displacement covered = 10 + 0 - 10 - 10 + 10

Total displacement covered = 0 m.

NOTE : Here area under the graph should not be calculated as area under s-t graph gives velocity but not displacement.

Answer 2

$\orange{\sf Find} \begin{cases} \sf\mapsto \pink{ distance \: covered \: at \: the \: end \: of \: 12seconds} \\ \sf\mapsto \red{ displacement \: covered \: at \: the \: end \: of \: 12seconds}\end{cases}$

$\orange{\sf Solution}$

➥Distance covered in first 2 seconds = 10m

➥Here, Body is in rest between 2 to 6 seconds so distance = 0m

➥Distance covered in first 6 to 8 seconds = 10m

➥Distance covered in first 8 to 10 seconds = 10m

➥ Distance covered in first 10 to 12 seconds = 10m

➟Hence, final distance will be

⇛ 10 + 10 + 10 + 10 = 40

⇨Here, Body is start at 0 seconds and comes to same position at 12th seconds so displacement is zero.

$\rule{300}{3}$

$\underline{\boxed{\sf Solution}}$

$\underline{\red{\sf distance \: covered \: in \: 12seconds = 40m}}$

$\underline{\orange{\sf displacement \: covered \: in \: 12seconds = 0m}}$