Question

The figure shown above shows time-velocity graph for a body in motion along a straight line. (1) State the nature of motion. (2) Find the total displacement of the body. (3) Find the acceleration from (0-3)sec and 3 to 5 sec. ​

Answer 1

1. Nature of Motion

According to the graph, The motion of the body plotted is of non-uniform motion. Because, In a uniform motion, Velocity of body remains the same(constant) throughout the whole journey.

2. Total Displacement of the body

Displacement is the shortest distance from final and initial point. We know,

Displacement of a body in velocity-time graph is the area of the graph.

Here, The figure is in the form of triangle, So

We have,

• Base = 5 units
• Height = 4 units

So,

⇒ Displacement = Area of triangle

⇒ Displacement = 1/2 × Base × Height

⇒ Displacement = 1/2 × 5 × 4

⇒ Displacement = 10 m.

3.a Acceleration from 0-3 seconds,

From 0 to 3 seconds, we have

• Change in Velocity = 4 - 0 = 4 m/s
• Time = 3 seconds

So,

⇒ Acceleration = Change in Velocity / Time

⇒ Acceleration = 4 / 3

⇒ Acceleration = 1.3 m/s²

3.b Acceleration from 3 to 5 seconds,

From 3 to 5 seconds, we have

• Change in velocity = 0 - 4 = -4 m/s
• Time = 5 - 3 = 2 seconds

Therefore,

⇒ Acceleration = Change in Velocity / Time

⇒ Acceleration = -4 / 2

⇒ Acceleration = -2 m/s²

Answer 2

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Nature \: of \: the \: motion}}}}$

According to the graph the motion of the body plotted is of non - uniform motion because in uniform motion ,velocity of a body remains the same constant the what the whole journey.

${\bigstar}\large{\boxed{\sf{\pink{Total \: displacement \: of \: the \: body}}}}$

Displacement is the shortest distance from initial point and the final point.

We know that,

Displacement of a body in velocity time graph is that area of the graph.

The figure is in the form of triangle ∆.

So, we have

• Base = 5 unit
• Height = 4 unit

So Displacement = Area of ∆

Displacement = 1/2 × Base × Height

Displacement = 1/2 × 5 × 4

Displacement = 10 metres

${\bigstar}\large{\boxed{\sf{\pink{Displacement \: from \: 0-3 \: second}}}}$

From 0-3 second we have

• Change in velocity = 4-0 = 4 m/s
• Time = 3 seconds

So,

Acceleration = Change in time / velocity

Acceleration = 4/3

Acceleration =1.3 m/s²

${\bigstar}\large{\boxed{\sf{\pink{Acceleration \: from \: 3-5 \: second}}}}$

From 3 to 5 seconds we have

• Change in velocity = 0-4 = -4 m/s
• Time = 5-3 = 2m/s

Therefore,

Acceleration = Change in velocity / time

Acceleration = -4/2

Acceleration = -2 m/s

Hope it's helpful

Thank you :)