(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by ca

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(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by car $B$ in time $t$ with initial velocity $u = 70 \text{ km/h}$ and deceleration $a = -20 \text{ km/h}^2$ is $d_B = 70t - \frac{1}{2} \times 20 \times t^2$.Since car $B$ is $2.5 \text{ km}$ behind car $A$,the condition for catching up is $d_B = d_A + 2.5$.Substituting the expressions: $70t - 10t^2 = 60t + 2.5$.Rearranging the terms: $10t^2 - 10t + 2.5 = 0$.Dividing by $10$: $t^2 - t + 0.25 = 0$.This is a perfect square: $(t - 0.5)^2 = 0$.Therefore,$t = 0.5 \text{ hours}$.

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

Medium

$A$ car $A$ is travelling on a straight level road with a uniform speed of $60 \text{ km/h}$. It is followed by another car $B$ which is moving with a speed of $70 \text{ km/h}$. When the distance between them is $2.5 \text{ km}$,the car $B$ is given a deceleration of $20 \text{ km/h}^2$. After how much time will $B$ catch up with $A$ in hours?

A
$1$
B
$0.5$
C
$0.25$
D
$1/8$

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Class 11 Questions

Class 11

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Chapter

Motion in a Straight Line

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Relative Motion in One Dimension

$A$ train is running at a constant speed of $90 \,km/h$ on a straight track. $A$ person standing on the top of a bogie moves in the direction of motion of the train such that he covers $1 \,m$ on the train each second. The speed of the person with respect to the ground is .........

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Two cars are moving in the same direction with a speed of $30 \, km/h$. They are separated from each other by $5 \, km$. $A$ third car moving in the opposite direction meets the two cars after an interval of $4 \, minutes$. The speed of the third car is .......... $km/h$.

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$A$ $210 \ m$ long train is moving due North at a speed of $25 \ m/s$. $A$ small bird is flying due South a little above the train with a speed of $5 \ m/s$. The time taken by the bird to cross the train is $........ \ s$.

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$A$ stone falls from the top of a tower of height $100 \text{ m}$ and at the same time another stone is projected vertically upwards from the ground with a velocity $25 \text{ m/s}$. The two stones meet after (in $\text{ s}$)

DifficultMHT CET 2026

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$A$ student is standing at a distance of $50 \, m$ from the bus. As soon as the bus begins its motion with an acceleration of $1 \, m/s^2$,the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road,the minimum value of $u$,so that the student is able to catch the bus is.........$m/s$.

DifficultAIIMS 2010

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$A$ train is running at a constant speed of $90 \,km/h$ on a straight track. $A$ person standing on the top of a bogie moves in the direction of motion of the train such that he covers $1 \,m$ on the train each second. The speed of the person with respect to the ground is .........

Two cars are moving in the same direction with a speed of $30 \, km/h$. They are separated from each other by $5 \, km$. $A$ third car moving in the opposite direction meets the two cars after an interval of $4 \, minutes$. The speed of the third car is .......... $km/h$.

$A$ $210 \ m$ long train is moving due North at a speed of $25 \ m/s$. $A$ small bird is flying due South a little above the train with a speed of $5 \ m/s$. The time taken by the bird to cross the train is $........ \ s$.

$A$ stone falls from the top of a tower of height $100 \text{ m}$ and at the same time another stone is projected vertically upwards from the ground with a velocity $25 \text{ m/s}$. The two stones meet after (in $\text{ s}$)

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