Question

The position - time graph of two objects A and B are shown below.
(a) Which body has greater velocity?
(b) Find the ratio of velocities of A and B.​

Answer 1

Answer:

a) A

b) $\sqrt3$ : 1/$\sqrt3$

Step-by-step explanation:

a) A, because tan 60 is greater than tan 30

b) tan 60 = $\sqrt3$

tan 30 = 1/$\sqrt3$

so ratio = $\sqrt{3\\}$ : 1/$\sqrt{3}$

Answer 2

(a) Object A will have greater slope and hence greater velocity.

(b) Ratio of velocities of A and B $=\sqrt{3} *\sqrt{3} =3$

Step-by-step explanation:

• Position-Time graph gives information about the motion of the object.
• Slope of position-time graph gives the speed or velocity of object.
• Velocity is defined as the rate of change in position of the object with respect to time.
• Slope of the graph $=m=tan \alpha$
• α is the angle made by the straight line plot with the positive x-axis.

Here slope of object A:

$m_{A} =tan 60^{o} \\m_{A}=\sqrt{3}$

Slope of B:

$m_{B}=tan 30^{o} \\m_{B}=1/\sqrt{3}$

(a) Velocity will be greater for the object with greater slope.

So, object A will have greater slope and hence greater velocity.

(b)Velocity of A$=m_{A}=\sqrt{3}$

Velocity of B$=m_{B}=1/\sqrt{3}$

Ratio of velocities of A and B $=\sqrt{3} *\sqrt{3} =3$