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PHXI03:MOTION IN A STRAIGHT LINE

362189 Assertion :
The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason :
Velocity is a vector quantity and speed is a scalar quantity.

1 Both assertion and reason are correct and reason is the correct explanation of assertion

2 Both assertion and reason are correct but reason is not the correct explanation of assertion

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362190 A particle is projected vertically upward with velocity $u$ from a point $A$ , when it returns to the point of projection

1 Its average speed is

u / 2

2 Average velocity is

u

3 Distance covered is zero

4 Its average speed is

u

Explanation:

The average speed $= \frac{2 H}{T} = \frac{T o t a l d i s t a n c e}{T i m e o f f l i g h t}$
$H = \frac{u^{2}}{2 g}$ (maximum height reached by the body)
$T = \frac{2 u}{g}$ (Time of flight)
$A v e r a g e s p e e d = \frac{2 \cdot \frac{u^{2}}{2 g}}{(\frac{2 u}{g})} = \frac{u}{2}$

PHXI03:MOTION IN A STRAIGHT LINE

362191 A particle having time period (in its circular motion) $π s,$ completes half revolution. Its mean speed is [given Radius of circle $= 100 c m$ ]

1

2.6 m / s

2

1.5 m / s

3

2.0 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2}$
= $\frac{π \times 1}{π / 2}$ = $2.0 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362192 Velocity of a body is given in the graph. Find the average speed and average velocity of the body from $t = 0 s$ to $12 s$
supporting img

1

\frac{8}{3} m / s, 0

2

\frac{4}{3} m / s, \frac{8}{3} m / s

3

\frac{16}{3} m / s, \frac{8}{3} m / s

4

0, \frac{16}{3} m / s

Explanation:

From $t = 0 s t o 6 s$ the body is travelling in one direction.
From $t = 0 s t o 12 s$ the body changes its direction at $t = 6 s$
$D i s t a n c e = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$+ [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 32 m$
$D i s p l a c e m e n t = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$- [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 0$
$A v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{t i m e} = \frac{0}{12 s} = 0$
$A v e r a g e s p e e d = \frac{D i s t a n c e}{t i m e} = \frac{32 m}{12 s} = \frac{8}{3} m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362189 Assertion :
The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason :
Velocity is a vector quantity and speed is a scalar quantity.

1 Both assertion and reason are correct and reason is the correct explanation of assertion

2 Both assertion and reason are correct but reason is not the correct explanation of assertion

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362190 A particle is projected vertically upward with velocity $u$ from a point $A$ , when it returns to the point of projection

1 Its average speed is

u / 2

2 Average velocity is

u

3 Distance covered is zero

4 Its average speed is

u

Explanation:

The average speed $= \frac{2 H}{T} = \frac{T o t a l d i s t a n c e}{T i m e o f f l i g h t}$
$H = \frac{u^{2}}{2 g}$ (maximum height reached by the body)
$T = \frac{2 u}{g}$ (Time of flight)
$A v e r a g e s p e e d = \frac{2 \cdot \frac{u^{2}}{2 g}}{(\frac{2 u}{g})} = \frac{u}{2}$

PHXI03:MOTION IN A STRAIGHT LINE

362191 A particle having time period (in its circular motion) $π s,$ completes half revolution. Its mean speed is [given Radius of circle $= 100 c m$ ]

1

2.6 m / s

2

1.5 m / s

3

2.0 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2}$
= $\frac{π \times 1}{π / 2}$ = $2.0 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362192 Velocity of a body is given in the graph. Find the average speed and average velocity of the body from $t = 0 s$ to $12 s$
supporting img

1

\frac{8}{3} m / s, 0

2

\frac{4}{3} m / s, \frac{8}{3} m / s

3

\frac{16}{3} m / s, \frac{8}{3} m / s

4

0, \frac{16}{3} m / s

Explanation:

From $t = 0 s t o 6 s$ the body is travelling in one direction.
From $t = 0 s t o 12 s$ the body changes its direction at $t = 6 s$
$D i s t a n c e = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$+ [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 32 m$
$D i s p l a c e m e n t = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$- [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 0$
$A v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{t i m e} = \frac{0}{12 s} = 0$
$A v e r a g e s p e e d = \frac{D i s t a n c e}{t i m e} = \frac{32 m}{12 s} = \frac{8}{3} m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362189 Assertion :
The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason :
Velocity is a vector quantity and speed is a scalar quantity.

1 Both assertion and reason are correct and reason is the correct explanation of assertion

2 Both assertion and reason are correct but reason is not the correct explanation of assertion

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362190 A particle is projected vertically upward with velocity $u$ from a point $A$ , when it returns to the point of projection

1 Its average speed is

u / 2

2 Average velocity is

u

3 Distance covered is zero

4 Its average speed is

u

Explanation:

The average speed $= \frac{2 H}{T} = \frac{T o t a l d i s t a n c e}{T i m e o f f l i g h t}$
$H = \frac{u^{2}}{2 g}$ (maximum height reached by the body)
$T = \frac{2 u}{g}$ (Time of flight)
$A v e r a g e s p e e d = \frac{2 \cdot \frac{u^{2}}{2 g}}{(\frac{2 u}{g})} = \frac{u}{2}$

PHXI03:MOTION IN A STRAIGHT LINE

362191 A particle having time period (in its circular motion) $π s,$ completes half revolution. Its mean speed is [given Radius of circle $= 100 c m$ ]

1

2.6 m / s

2

1.5 m / s

3

2.0 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2}$
= $\frac{π \times 1}{π / 2}$ = $2.0 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362192 Velocity of a body is given in the graph. Find the average speed and average velocity of the body from $t = 0 s$ to $12 s$
supporting img

1

\frac{8}{3} m / s, 0

2

\frac{4}{3} m / s, \frac{8}{3} m / s

3

\frac{16}{3} m / s, \frac{8}{3} m / s

4

0, \frac{16}{3} m / s

Explanation:

From $t = 0 s t o 6 s$ the body is travelling in one direction.
From $t = 0 s t o 12 s$ the body changes its direction at $t = 6 s$
$D i s t a n c e = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$+ [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 32 m$
$D i s p l a c e m e n t = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$- [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 0$
$A v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{t i m e} = \frac{0}{12 s} = 0$
$A v e r a g e s p e e d = \frac{D i s t a n c e}{t i m e} = \frac{32 m}{12 s} = \frac{8}{3} m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362189 Assertion :
The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason :
Velocity is a vector quantity and speed is a scalar quantity.

1 Both assertion and reason are correct and reason is the correct explanation of assertion

2 Both assertion and reason are correct but reason is not the correct explanation of assertion

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362190 A particle is projected vertically upward with velocity $u$ from a point $A$ , when it returns to the point of projection

1 Its average speed is

u / 2

2 Average velocity is

u

3 Distance covered is zero

4 Its average speed is

u

Explanation:

The average speed $= \frac{2 H}{T} = \frac{T o t a l d i s t a n c e}{T i m e o f f l i g h t}$
$H = \frac{u^{2}}{2 g}$ (maximum height reached by the body)
$T = \frac{2 u}{g}$ (Time of flight)
$A v e r a g e s p e e d = \frac{2 \cdot \frac{u^{2}}{2 g}}{(\frac{2 u}{g})} = \frac{u}{2}$

PHXI03:MOTION IN A STRAIGHT LINE

362191 A particle having time period (in its circular motion) $π s,$ completes half revolution. Its mean speed is [given Radius of circle $= 100 c m$ ]

1

2.6 m / s

2

1.5 m / s

3

2.0 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2}$
= $\frac{π \times 1}{π / 2}$ = $2.0 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362192 Velocity of a body is given in the graph. Find the average speed and average velocity of the body from $t = 0 s$ to $12 s$
supporting img

1

\frac{8}{3} m / s, 0

2

\frac{4}{3} m / s, \frac{8}{3} m / s

3

\frac{16}{3} m / s, \frac{8}{3} m / s

4

0, \frac{16}{3} m / s

Explanation:

From $t = 0 s t o 6 s$ the body is travelling in one direction.
From $t = 0 s t o 12 s$ the body changes its direction at $t = 6 s$
$D i s t a n c e = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$+ [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 32 m$
$D i s p l a c e m e n t = [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4]$
$- [\frac{1}{2} \times 2 \times 4 + 2 \times 4 + \frac{1}{2} \times 2 \times 4] = 0$
$A v e r a g e v e l o c i t y = \frac{D i s p l a c e m e n t}{t i m e} = \frac{0}{12 s} = 0$
$A v e r a g e s p e e d = \frac{D i s t a n c e}{t i m e} = \frac{32 m}{12 s} = \frac{8}{3} m / s$

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