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प्रश्न
A driver of a car travelling at 52 km h−1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h−1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
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उत्तर
The data given in this numerical problem are in different units. So, we should first convert km h-1 unit into m s-1 unit.
For first car:
Initial velocity u = 52 km h-1
= `(52 "km")/(1 "h")`
= `(52 xx 1000 "m")/(1 xx 3600 "s")`
= 14.4 s-1
Final velocity, v = 0 km h-1 = 0.0 m s-1
Time taken, t = 5s
For second car:
Initial velocity, u = 3 km h-1
= `(3 "km")/(1"h")`
= `(3 xx 1000 "m")/(1 xx 3600 "s")`
= 0.8 ms-1
Final velocity, v = 0 km h-1 = 0.0 m s-1
Time taken, t = 10s
The area under a moving body's speed-time graph indicates the distance it has traveled.
So, Distance travelled by the first car = Area of the triangle AOB
= `1/2 xx "OB" xx "AO"`
= `1/2 xx 14.4` ms-1 × 5s
= `1/2 xx 14.4 xx 5 "m"`
= 36 m
Similarly, distance travelled by the second car = area of triangle COD.
= `1/2 xx "OD" xx "CO"`
= `1/2 xx 0.83 m s^-1 xx 10 s`
= `1/2 xx 0.83 xx 10 "m"`
= 4.1 m
Thus, the second car travels 4.1 m and the first car travels 36 m before coming to rest.
So, the first car travelled farther after the brakes were applied.
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संबंधित प्रश्न
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Show the shape of the distance-time graph for the motion in the following case:
A car moving with a constant speed.
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A student draws a distance-time graph for a moving scooter and finds that a section of the graph is horizontal line parallel to the time axis. Which of the following conclusion is correct about this section of the graph?
Figure (a) shows the displacement-time graph for the motion of a body. Use it to calculate the velocity of the body at t = 1 s, 2 s and 3 s, and then draw the velocity-time graph in Figure (b) for it.
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| (a) | (b) |
A spaceship is moving in space with a velocity of 60 kms−1. It fires its retro engines for 20 seconds and velocity is reduced to 55 kms−1. Calculate the distance travelled by a spaceship in 40 s, from the time of firing of the retro- rockets.
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What do you infer if
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