(D) The speed of the thief's jeep is $v_t = 9 \, m/s$.The speed of the policeman's motorcycle is $v_p = 10 \, m/s$.The relative speed of the policeman

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(D) The speed of the thief's jeep is $v_t = 9 \, m/s$.The speed of the policeman's motorcycle is $v_p = 10 \, m/s$.The relative speed of the policeman with respect to the thief is $v_{rel} = v_p - v_t = 10 - 9 = 1 \, m/s$.The initial distance (separation) between them is $d = 100 \, m$.To catch the thief,the policeman must cover this relative distance at the relative speed.Time taken $t = \frac{d}{v_{rel}} = \frac{100 \, m}{1 \, m/s} = 100 \, s$.Therefore,it will take $100 \, seconds$ for the policeman to catch the thief.

Class 11 Physics Motion in a Straight Line Relative Motion in One Dimension

Difficult

$A$ thief is running away on a straight road in a jeep moving with a speed of $9 \, m/s$. $A$ policeman chases him on a motorcycle moving at a speed of $10 \, m/s$. If the instantaneous separation between the jeep and the motorcycle is $100 \, m$,how long will it take for the policeman to catch the thief?

A
$1$
B
$19$
C
$90$
D
$100$

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Motion in a Straight Line

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Relative Motion in One Dimension

$A$ bird flies to and fro between two cars which move towards each other with velocities $v_1 = 20\, m/s$ and $v_2 = 30\, m/s$. If the speed of the bird is $v_3 = 10\, m/s$ and the initial distance of separation between them is $d = 2\, km$,find the total distance covered by the bird until the cars meet. (in $, m$)

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Two cars $A$ and $B$ are travelling in the same direction with velocities $v_1$ and $v_2$ $(v_1 > v_2)$. When car $A$ is at a distance $d$ ahead of car $B$,the driver of car $A$ applies the brake,producing a uniform retardation $a$. There will be no collision when:

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$A$ train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains is $x$,what should be the minimum retardation of the train to avoid a collision?

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What are the speeds of two objects if,when they move uniformly towards each other,they get $4\,m$ closer in each second and when they move uniformly in the same direction with the original speeds,they get $4.0\,m$ closer each $10\,s$?

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$A$ man is at a distance $d$ behind a bus. The bus starts from rest and moves away from the man with a constant acceleration $a$. At the same time,the man starts running towards the bus with a constant velocity $v$. Which of the following statements are correct?

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Two cars $A$ and $B$ are travelling in the same direction with velocities $v_1$ and $v_2$ $(v_1 > v_2)$. When car $A$ is at a distance $d$ ahead of car $B$,the driver of car $A$ applies the brake,producing a uniform retardation $a$. There will be no collision when:

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