motion in straight line

physics part i

physics

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A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the *x*-*t *graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

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On a two-lane road, car A is travelling with a speed of 36 km h^{-1}. Two cars B and C approach car A in opposite directions with a speed of 54 km h^{-1} each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident ?

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Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h–1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s–2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them ?

In case of train A:

Initial velocity, *u* = 72 km/h = 20 m/s

Time, *t* = 50 s

Since the train is moving with uniform velocity,

Acceleration, *a*_{I} = 0

Now, using second equation of motion,

Distance covered by train A is given by,

For train B,

Initial velocity, u_{B} = 72 km/h = 20 m/s

Acceleration, *a* = 1 m/s^{2 }

Time,* t* = 50 s

Now, using second equation of motion,

Distance travelled by second train B is,

Length of both trains = 2

Therefore, the original distance between the driver of train A and the guard of train B = 2250 - 1000 - 800

= 450m.

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A jet airplane travelling at the speed of 500 km h^{–1} ejects its products of combustion at the speed of 1500 km h^{–1} relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ?

Negative sign implies that the direction of its products of combustion is opposite to the direction of motion of the jet airplane.

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