At metro station, a girl walks up a stationary escalator in time $t_{1}$ . If she remains stationary on escalator, then the escalator take her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be:

$\frac{( t _{1} + t _{2} )}{2}$

$\frac{( t _{1} t _{2} )}{( t _{1} - t _{2} )}$

$\frac{( t _{1} t _{2} )}{( t _{1} + t _{2} )}$

$(t_{1} - t_{2})$

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A tourist being chased by an energy bear is running in a straight line towards his car at a speed of $4.0 m / s$ . The car is a distance $d$ away. The bear is $26 m$ behind the tourist and running at $6.0 m / s$ . The tourist reaches the car safely the maximum possible value for $d$ is:-

$25 m$

$26 m$

$52 m$

$50 m$

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A horizontal plane supports a stationary vertical cylinder of radius $R$ and a disc $A$ attached to the cylinder by a horizontal thread $A B$ of length $ℓ_{0}$ . An initial velocity $V_{0}$ is imparted to the disc as shown in the figure. Time taken by if until it strike against the cylinder is $\frac{ℓ _{0}^{2}}{K V _{0} R}$ . Find the value of K is . (All the surface are smooth.)

$2$

$3$

$4$

$1$

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A particle $P^{'}$ is moving with a velocity $2 \hat{1}$ m/s with respect to an inertial frame $S_{0}$ . A frame of reference $S_{1}$ attached to a vehicle which moves with an acceleration $(4 \hat{1} + 3 \hat{j}) m / s^{2}$ with respect to $s^{0}$ . The velocity of particle $^{'} P^{'}$ with time as observed by the observer with $S_{1}$ is

$- 2 \hat{i} m / s$

$(- 4 \hat{1} + 3 \hat{j}) t$ m/s$$

$(2 \hat{i} + (4 \hat{i} + 3 \hat{1}) t) m / s$

$(2 - 4 t) \hat{i} m / s - 3 t \hat{j} m / s$

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A bucket placed in the open where the rain is falling vertically. If a wind begins to blow horizontally at double the velocity of the rain, how will the rate of filling of the bucket change?

Remain unchanged

Doubled

Halved

Become fourtimes

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A lift starts from the top of a mine shaft and descends with a constant speed of $10 m / s$ . $4$ sec later a boy throws a stone vertically upwards from the top of the shaft with a speed of $30 m / s$ . If stone hits the lift at a distance $x$ below the shaft write the value of $\frac{x}{3}$ (in m)
[Take: $g = 10 m / s^{2}$ ] (given value of $206 = 49$ )

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A stationary boat having mass $4 m$ at the surface of a pond. If a man of mass $m$ jumps out from the boat with velocity $V$ , then velocity of boat after jumping is

$- \frac{V}{4}$

$\frac{V}{5}$

$- \frac{V}{5}$

$- \frac{4 V}{5}$

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Three point $A, B, C$ are located in a straight line $A B = a$ and $A C = b$ . Two particles start from point $B$ and $C$ and move with uniform velocities $V_{1}$ and $V_{2}$ respectively such that angle between $V_{1}$ and line $A B C$ and $V_{2}$ and $A B C$ is $θ$ . If point $A$ and both particles have always in a straight line then:

$a V_{1} = b V_{2}$

$a V_{1}^{2} = b V_{2}^{2}$

$a^{2} V_{1} = b^{2} V_{2}$

$a V_{2} = b V_{1}$

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Two cars are moving in the same direction with the same speed 30 km/h. They are separated by a distance of 4 km. What is the speed of a car moving in the opposite direction if it meets these two cars at an interval of 5 min?

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A 100 m long train crosses a man travelling at 5 km/hr, in opposite direction in 7.2 seconds, then the velocity of train is :-

40 km/hr

25 km/hr

20 km/hr

45 km/hr

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Here Are 25 Questions For You To Practice For Free!.

Testing Purpose

At metro station, a girl walks up a stationary escalator in time $t_{1}$ . If she remains stationary on escalator, then the escalator take her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be:

$\frac{( t _{1} + t _{2} )}{2}$

$\frac{( t _{1} t _{2} )}{( t _{1} - t _{2} )}$

$\frac{( t _{1} t _{2} )}{( t _{1} + t _{2} )}$

$(t_{1} - t_{2})$

A tourist being chased by an energy bear is running in a straight line towards his car at a speed of $4.0 m / s$ . The car is a distance $d$ away. The bear is $26 m$ behind the tourist and running at $6.0 m / s$ . The tourist reaches the car safely the maximum possible value for $d$ is:-

$25 m$

$26 m$

$52 m$

$50 m$

$2$

$3$

$4$

$1$

$- 2 \hat{i} m / s$

$(- 4 \hat{1} + 3 \hat{j}) t$ m/s$$

$(2 \hat{i} + (4 \hat{i} + 3 \hat{1}) t) m / s$

$(2 - 4 t) \hat{i} m / s - 3 t \hat{j} m / s$

A bucket placed in the open where the rain is falling vertically. If a wind begins to blow horizontally at double the velocity of the rain, how will the rate of filling of the bucket change?

Remain unchanged

Doubled

Halved

Become fourtimes

A stationary boat having mass $4 m$ at the surface of a pond. If a man of mass $m$ jumps out from the boat with velocity $V$ , then velocity of boat after jumping is

$- \frac{V}{4}$

$\frac{V}{5}$

$- \frac{V}{5}$

$- \frac{4 V}{5}$

$a V_{1} = b V_{2}$

$a V_{1}^{2} = b V_{2}^{2}$

$a^{2} V_{1} = b^{2} V_{2}$

$a V_{2} = b V_{1}$

Two cars are moving in the same direction with the same speed 30 km/h. They are separated by a distance of 4 km. What is the speed of a car moving in the opposite direction if it meets these two cars at an interval of 5 min?

A 100 m long train crosses a man travelling at 5 km/hr, in opposite direction in 7.2 seconds, then the velocity of train is :-

40 km/hr

25 km/hr

20 km/hr

45 km/hr

Here Are 25 Questions For You To Practice For Free!.

Testing Purpose

At metro station, a girl walks up a stationary escalator in time t1​. If she remains stationary on escalator, then the escalator take her up in time t2​. The time taken by her to walk up on the moving escalator will be:

2(t1​+t2​)​

(t1​−t2​)(t1​t2​)​

(t1​+t2​)(t1​t2​)​

(t1​−t2​)

A tourist being chased by an energy bear is running in a straight line towards his car at a speed of 4.0 m/s. The car is a distance d away. The bear is 26 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely the maximum possible value for d is:-

25 m

26 m

52 m

50 m

2

3

4

1

A particle P′ is moving with a velocity 21^ m/s with respect to an inertial frame S0​. A frame of reference S1​ attached to a vehicle which moves with an acceleration (41^+3j^​)m/s2 with respect to s0. The velocity of particle ′P′ with time as observed by the observer with S1​ is

−2i^m/s

(−41^+3j^​)tm/s$$

(2i^+(4i^+31^)t)m/s

(2−4t)i^m/s−3tj^​m/s

A bucket placed in the open where the rain is falling vertically. If a wind begins to blow horizontally at double the velocity of the rain, how will the rate of filling of the bucket change?

Remain unchanged

Doubled

Halved

Become fourtimes

A stationary boat having mass 4m at the surface of a pond. If a man of mass m jumps out from the boat with velocity V, then velocity of boat after jumping is

−4V​

5V​

−5V​

−54V​

Three point A,B,C are located in a straight line AB=a and AC=b. Two particles start from point B and C and move with uniform velocities V1​ and V2​ respectively such that angle between V1​ and line ABC and V2​ and ABC is θ. If point A and both particles have always in a straight line then:

aV1​=bV2​

aV12​=bV22​

a2V1​=b2V2​

aV2​=bV1​

Two cars are moving in the same direction with the same speed 30 km/h. They are separated by a distance of 4 km. What is the speed of a car moving in the opposite direction if it meets these two cars at an interval of 5 min?

A 100 m long train crosses a man travelling at 5 km/hr, in opposite direction in 7.2 seconds, then the velocity of train is :-

40 km/hr

25 km/hr

20 km/hr

45 km/hr

At metro station, a girl walks up a stationary escalator in time $t_{1}$ . If she remains stationary on escalator, then the escalator take her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be:

$\frac{( t _{1} + t _{2} )}{2}$

$\frac{( t _{1} t _{2} )}{( t _{1} - t _{2} )}$

$\frac{( t _{1} t _{2} )}{( t _{1} + t _{2} )}$

$(t_{1} - t_{2})$

A tourist being chased by an energy bear is running in a straight line towards his car at a speed of $4.0 m / s$ . The car is a distance $d$ away. The bear is $26 m$ behind the tourist and running at $6.0 m / s$ . The tourist reaches the car safely the maximum possible value for $d$ is:-

$25 m$

$26 m$

$52 m$

$50 m$

$2$

$3$

$4$

$1$

$- 2 \hat{i} m / s$

$(- 4 \hat{1} + 3 \hat{j}) t$ m/s$$

$(2 \hat{i} + (4 \hat{i} + 3 \hat{1}) t) m / s$

$(2 - 4 t) \hat{i} m / s - 3 t \hat{j} m / s$

A stationary boat having mass $4 m$ at the surface of a pond. If a man of mass $m$ jumps out from the boat with velocity $V$ , then velocity of boat after jumping is

$- \frac{V}{4}$

$\frac{V}{5}$

$- \frac{V}{5}$

$- \frac{4 V}{5}$

$a V_{1} = b V_{2}$

$a V_{1}^{2} = b V_{2}^{2}$

$a^{2} V_{1} = b^{2} V_{2}$

$a V_{2} = b V_{1}$