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PHXI03:MOTION IN A STRAIGHT LINE

362202 A car moves from $A$ to $B$ with a speed of 30 $k m p h$ and from $B$ to $A$ with a speed of 20 $k m p h$ . What is the average speed of the car?

1

50 k m p h

2

25 k m p h

3

10 k m p h

4

24 k m p h

Explanation:

Let $S$ be distance between $A$ and $B$ .
Let $t_{1}$ be time taken by the car to move from $A$ to $B$ with speed $v_{1}$ and $t_{2}$ be time taken by the car to move from $B$ to $A$ with speed $v_{2}$ . Then
$t_{1} = \frac{S}{v_{1}} a n d t_{2} = \frac{S}{v_{2}}$
Average speed of the car
$v_{a v g} = \frac{T o t a l d i s t a n c e t r a v e l l e d}{T o t a l t i m e t a k e n} = \frac{2 S}{t_{1} + t_{2}}$
$= \frac{2 S}{\frac{S}{v_{1}} + \frac{S}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Here, $v_{1} = 30 k m p h, v_{2} = 20 k m p h$
$∴ v_{a v g} = \frac{2 \times 30 \times 20}{30 + 20} = 24 k m p h$

KCET - 2014

PHXI03:MOTION IN A STRAIGHT LINE

362203 A particle having time period (in its circular motion) $2 π s$ completes half revolution. Its mean speed is [given Radius of circle $= 50 c m$ ]

1

1.5 m / s

2

2.6 m / s

3

0.5 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2} = \frac{π \times 0.5}{π} = 0.5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362204 The velocity of a body as a function of time is $v = 10 - 5 t$ . Find the average velocity of the body in the time interval from $0 s t o 2 s$ .

1

0

2

5 m / s

3

10 m / s

4

20 m / s

Explanation:

Given that $v = 10 - 5 t$
The average velocity is $⟨ v ⟩ = \frac{\int_{0}^{2} (10 - 5 t) d t}{2 - 0}$
$⟨ v ⟩ = \frac{1}{2} [\int_{0}^{2} 10 d t - 5 \int_{0}^{2} t d t)] = 5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362205 Assertion :
The speedometer of an automobile measures the average speed of the automobile.
Reason :
Average velocity is equal to total displacement per total time taken.

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.

Explanation:

Speed meter measures instantaneous speed of automobile. $v_{a v g} = \frac{Δ s}{Δ t}$
So option (4) is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362202 A car moves from $A$ to $B$ with a speed of 30 $k m p h$ and from $B$ to $A$ with a speed of 20 $k m p h$ . What is the average speed of the car?

1

50 k m p h

2

25 k m p h

3

10 k m p h

4

24 k m p h

Explanation:

Let $S$ be distance between $A$ and $B$ .
Let $t_{1}$ be time taken by the car to move from $A$ to $B$ with speed $v_{1}$ and $t_{2}$ be time taken by the car to move from $B$ to $A$ with speed $v_{2}$ . Then
$t_{1} = \frac{S}{v_{1}} a n d t_{2} = \frac{S}{v_{2}}$
Average speed of the car
$v_{a v g} = \frac{T o t a l d i s t a n c e t r a v e l l e d}{T o t a l t i m e t a k e n} = \frac{2 S}{t_{1} + t_{2}}$
$= \frac{2 S}{\frac{S}{v_{1}} + \frac{S}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Here, $v_{1} = 30 k m p h, v_{2} = 20 k m p h$
$∴ v_{a v g} = \frac{2 \times 30 \times 20}{30 + 20} = 24 k m p h$

KCET - 2014

PHXI03:MOTION IN A STRAIGHT LINE

362203 A particle having time period (in its circular motion) $2 π s$ completes half revolution. Its mean speed is [given Radius of circle $= 50 c m$ ]

1

1.5 m / s

2

2.6 m / s

3

0.5 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2} = \frac{π \times 0.5}{π} = 0.5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362204 The velocity of a body as a function of time is $v = 10 - 5 t$ . Find the average velocity of the body in the time interval from $0 s t o 2 s$ .

1

0

2

5 m / s

3

10 m / s

4

20 m / s

Explanation:

Given that $v = 10 - 5 t$
The average velocity is $⟨ v ⟩ = \frac{\int_{0}^{2} (10 - 5 t) d t}{2 - 0}$
$⟨ v ⟩ = \frac{1}{2} [\int_{0}^{2} 10 d t - 5 \int_{0}^{2} t d t)] = 5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362205 Assertion :
The speedometer of an automobile measures the average speed of the automobile.
Reason :
Average velocity is equal to total displacement per total time taken.

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.

Explanation:

Speed meter measures instantaneous speed of automobile. $v_{a v g} = \frac{Δ s}{Δ t}$
So option (4) is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362202 A car moves from $A$ to $B$ with a speed of 30 $k m p h$ and from $B$ to $A$ with a speed of 20 $k m p h$ . What is the average speed of the car?

1

50 k m p h

2

25 k m p h

3

10 k m p h

4

24 k m p h

Explanation:

Let $S$ be distance between $A$ and $B$ .
Let $t_{1}$ be time taken by the car to move from $A$ to $B$ with speed $v_{1}$ and $t_{2}$ be time taken by the car to move from $B$ to $A$ with speed $v_{2}$ . Then
$t_{1} = \frac{S}{v_{1}} a n d t_{2} = \frac{S}{v_{2}}$
Average speed of the car
$v_{a v g} = \frac{T o t a l d i s t a n c e t r a v e l l e d}{T o t a l t i m e t a k e n} = \frac{2 S}{t_{1} + t_{2}}$
$= \frac{2 S}{\frac{S}{v_{1}} + \frac{S}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Here, $v_{1} = 30 k m p h, v_{2} = 20 k m p h$
$∴ v_{a v g} = \frac{2 \times 30 \times 20}{30 + 20} = 24 k m p h$

KCET - 2014

PHXI03:MOTION IN A STRAIGHT LINE

362203 A particle having time period (in its circular motion) $2 π s$ completes half revolution. Its mean speed is [given Radius of circle $= 50 c m$ ]

1

1.5 m / s

2

2.6 m / s

3

0.5 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2} = \frac{π \times 0.5}{π} = 0.5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362204 The velocity of a body as a function of time is $v = 10 - 5 t$ . Find the average velocity of the body in the time interval from $0 s t o 2 s$ .

1

0

2

5 m / s

3

10 m / s

4

20 m / s

Explanation:

Given that $v = 10 - 5 t$
The average velocity is $⟨ v ⟩ = \frac{\int_{0}^{2} (10 - 5 t) d t}{2 - 0}$
$⟨ v ⟩ = \frac{1}{2} [\int_{0}^{2} 10 d t - 5 \int_{0}^{2} t d t)] = 5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362205 Assertion :
The speedometer of an automobile measures the average speed of the automobile.
Reason :
Average velocity is equal to total displacement per total time taken.

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.

Explanation:

Speed meter measures instantaneous speed of automobile. $v_{a v g} = \frac{Δ s}{Δ t}$
So option (4) is correct.

PHXI03:MOTION IN A STRAIGHT LINE

362202 A car moves from $A$ to $B$ with a speed of 30 $k m p h$ and from $B$ to $A$ with a speed of 20 $k m p h$ . What is the average speed of the car?

1

50 k m p h

2

25 k m p h

3

10 k m p h

4

24 k m p h

Explanation:

Let $S$ be distance between $A$ and $B$ .
Let $t_{1}$ be time taken by the car to move from $A$ to $B$ with speed $v_{1}$ and $t_{2}$ be time taken by the car to move from $B$ to $A$ with speed $v_{2}$ . Then
$t_{1} = \frac{S}{v_{1}} a n d t_{2} = \frac{S}{v_{2}}$
Average speed of the car
$v_{a v g} = \frac{T o t a l d i s t a n c e t r a v e l l e d}{T o t a l t i m e t a k e n} = \frac{2 S}{t_{1} + t_{2}}$
$= \frac{2 S}{\frac{S}{v_{1}} + \frac{S}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Here, $v_{1} = 30 k m p h, v_{2} = 20 k m p h$
$∴ v_{a v g} = \frac{2 \times 30 \times 20}{30 + 20} = 24 k m p h$

KCET - 2014

PHXI03:MOTION IN A STRAIGHT LINE

362203 A particle having time period (in its circular motion) $2 π s$ completes half revolution. Its mean speed is [given Radius of circle $= 50 c m$ ]

1

1.5 m / s

2

2.6 m / s

3

0.5 m / s

4

0.7 m / s

Explanation:

The average or Mean speed is
$⟨ v ⟩ = \frac{π R}{T / 2} = \frac{π \times 0.5}{π} = 0.5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362204 The velocity of a body as a function of time is $v = 10 - 5 t$ . Find the average velocity of the body in the time interval from $0 s t o 2 s$ .

1

0

2

5 m / s

3

10 m / s

4

20 m / s

Explanation:

Given that $v = 10 - 5 t$
The average velocity is $⟨ v ⟩ = \frac{\int_{0}^{2} (10 - 5 t) d t}{2 - 0}$
$⟨ v ⟩ = \frac{1}{2} [\int_{0}^{2} 10 d t - 5 \int_{0}^{2} t d t)] = 5 m / s$

PHXI03:MOTION IN A STRAIGHT LINE

362205 Assertion :
The speedometer of an automobile measures the average speed of the automobile.
Reason :
Average velocity is equal to total displacement per total time taken.

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.

Explanation:

Speed meter measures instantaneous speed of automobile. $v_{a v g} = \frac{Δ s}{Δ t}$
So option (4) is correct.