Relative Motion in One Dimension questions | Relative Motion in One Dimension jee questions

Q 1 :

Two cars are travelling towards each other at a speed of 20 ${ms}^{- 1}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 ${ms}^{- 2}$ . The distance between them when they come to rest is: [2024]

200 m
50 m
100 m
25 m

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2

3

4

(3)

$| {\vec{u}}_{B A} |$ $= 40 m/s$

$| {\vec{a}}_{B A} |$ $= 4 {m/s}^{2}$

Applying, $(v^{2} = u^{2} + 2 a s)_{relative}$

$0 = {(40)}^{2} + 2 (- 4) (s) \Rightarrow s = 200 m$

Remaining distance $= 300 - 200 = 100 m$

So, when both cars will stop then the distance between them, will be

$d = 300 - 200 = 100 m$

Q 2 :

Train A is moving along two parallel rail tracks towards north with speed 72 km/h, and train B is moving towards south with speed 108 km/h.

Velocity of train B with respect to A and velocity of ground with respect to B are (in ${ms}^{- 1}$ ) [2024]

−30 and 50
−50 and −30
−50 and 30
50 and −30

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2

3

4

(4)

$= 72 \times \frac{5}{18} = 20 m/s = 108 \times \frac{5}{18} = 30 m/s$

Velocity of train B with respect to train A

$V_{B A} = V_{B} - V_{A} = 30 - (- 20) = 50 m/s$

$[Taking South = +ve, North = -ve]$

Ground is at rest, so

$V_{G B} = V_{G} - V_{B}$

$= 0 - (30) = - 30 m/s$

Q 3 :

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is __________. [2025]

0%

(3)

For first car P $\to$ acceleration ( $a_{P}$ ) = ct, c is constant

For second car Q $\to$ acceleration ( $a_{Q}$ ) = a, a is constant

Let us analyse the problem in two cases

Case I:

$\Rightarrow$ $u_{Q P}$ and $a_{Q P}$ in same direction

They cross 2 times in this case

Case-II:

$a_{Q P}$ and $u_{Q P}$ in opposite direction

They cross 3 times in this case.

Q 4 :

Two trains $‘ A ’$ and $‘ B ’$ of length $' l'$ and $' 4 l'$ are travelling into a tunnel of length $' L'$ in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train ‘A’ takes 35 s less time than train ‘B’ to cross the tunnel then, length ‘L’ of tunnel is: (Given L = 60 $l$ ) [2023]

1200 m
2700 m
1800 m
900 m

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4

(3)

$\frac{60 ℓ + 4 ℓ}{20} - \frac{61 ℓ}{30} = 35$

$\Rightarrow ℓ = \frac{1050}{35}$

$\Rightarrow L = 60 ℓ = \frac{1050}{35} \times 60 = 1800 m$

Q 5 :

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is [2023]

80 m
200 m
120 m
320 m

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2

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4

(4)

Velocity of train A

$V_{A} = 90 \frac{km}{hr} = 90 \times \frac{5}{18} = 25 m/s$

Velocity of train B

$V_{B} = 54 \frac{km}{hr} = 54 \times \frac{5}{18} = 15 m/s$

Velocity of train B w.r.t. train A $= {\vec{V}}_{B} - {\vec{V}}_{A}$

$= 15 - (- 25) m/s = 40 m/s$

$Time of crossing = \frac{length of train}{relative velocity}$

$8 = \frac{ℓ}{40}$

$\Rightarrow l = 8 \times 40 = 320 meter$

Topic Question Set

Q 1 :

Two cars are travelling towards each other at a speed of 20 ${ms}^{- 1}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 ${ms}^{- 2}$ . The distance between them when they come to rest is: [2024]

Q 2 :

Train A is moving along two parallel rail tracks towards north with speed 72 km/h, and train B is moving towards south with speed 108 km/h.

Velocity of train B with respect to A and velocity of ground with respect to B are (in ${ms}^{- 1}$ ) [2024]

0%

Q 5 :

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is [2023]

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