Question

How far did the object travel by the end of eight seconds according to the graph above?

Answer 1

The right option is, it travels in 20 centimeter

Step-by-step explanation:

Speed-time graph:

Speed-time graph is a graph of speed against time.

The slope of the graph give the acceleration of the body. And the Area of the shape of the graph gives the total distance traveled by the body.

From the graph above the motion of the body can be divided into two sections,

Section A: The motion for the first 4 seconds

Section B: The motion for next 4 seconds.

Total distance covered by the body = Area of section A + Area of section B

The Shape of section A is rectangle

Area of a rectangle = L×B

Where L = Length, B= Breadth, from the graph L=(4-0) = 4 s and B = 1-(-2) = 3 cm/s

Area of section A = 4 × 3 = 12 cm

Also the area of the shape in section B is a rectangle.

Area of a rectangle = L × B.

from the graph, L=(8-4) = 4 s, B= 0-(-2) = 2 cm/s

Area of Section B = 4 × 2 = 8 cm

∴ Total Area traveled by the object after 8 seconds = 12+8 = 20 cm

The right option is, it travels in 20 centimeter

Answer 2

4

Step-by-step explanation:

In the speed vs time graph,the distance travelled by the object is the area under the speed-time curve.

So,area under the speed-time curve=
`\text{area in first 4 seconds+area in last 4 seconds}`

It is given that
`speed=1` in first four seconds.

`\text{area in first 4 seconds}=speed* time=1* 4=4`

It is given that
`speed=0` in last four seconds.

`\text{area in last 4 seconds}=speed* time=0* 4=0`

area under the speed-time curve=
`\text{area in first 4 seconds+area in last 4 seconds}`=
`4+0=4`