A driver of a car travelling at 52, km, h^{-1} applies brakes and accelerates uniformly in opposite

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hard

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 ?

Option A

Option B

Option C

Option D

Solution

As given in the figure below $PR$ and $SQ$ are the Speed-time graph for given two cars with initial speeds $52 \,km\,h^{-1}$ and $3\, km\,h^{-1}$ respectively.

Distance Travelled by first car before coming to rest $=$ Area of $\Delta OPR $

$=(1 / 2) \times OR \times OP$

$=(1 / 2) \times 5\, s \times 52\, km\,h^{ -1}$

$=(1 / 2) \times 5 \times(52 \times 1000) / 3600) \,m$

$=(1 / 2) \times 5 \times(130 / 9) \,m$

$=325 / 9 \,m$

$=36.11\, m$

Distance Travelled by second car before coming to rest $=$ Area of $\Delta OSQ $

$=(1 / 2) \times O Q \times OS$

$=(1 / 2) \times 10\, s \times 3 \,km\,h^{ -1}$

$=(1 / 2) \times 10 \times(3 \times 1000) / 3600) \,m$

$=(1 / 2) \times 10 \times(5 / 6) \,m$

$=5 \times(5 / 6)\, m$

$=25 / 6 \,m$

$=4.16\, m$

Standard 9

Science

Abdul, while driving to school, computes the average speed for his trip to be $20 \,km\,h^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $40\, km \,h^{-1}$. What is the average speed(in $km\,h ^{-1}$) for Abdul's trip?

hard

An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

medium

The speed-time graph for a car is shown is Fig.

$(a)$ Find how far does the car travel in the first $4,sec$. Shade the area on the graph that represents the distance travelled by the car during the period.

$(b)$ Which part of the graph represents uniform motion of the car ?

medium

A train is travelling at a speed of $90\, km \,h^{-1}$. Brakes are applied so as to produce a uniform acceleration of $- 0.5\, m s^{-2}$. Find how far(in $m$) the train will go before it is brought to rest.

medium

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easy

Solution

Similar Questions

Abdul, while driving to school, computes the average speed for his trip to be $20 \,km\,h^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $40\, km \,h^{-1}$. What is the average speed(in $km\,h ^{-1}$) for Abdul's trip?

An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

The speed-time graph for a car is shown is Fig. $(a)$ Find how far does the car travel in the first $4,sec$. Shade the area on the graph that represents the distance travelled by the car during the period. $(b)$ Which part of the graph represents uniform motion of the car ?

A train is travelling at a speed of $90\, km \,h^{-1}$. Brakes are applied so as to produce a uniform acceleration of $- 0.5\, m s^{-2}$. Find how far(in $m$) the train will go before it is brought to rest.

During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, $3 \times 10^{8}\,m\,s^{-1}$.

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The speed-time graph for a car is shown is Fig.

$(a)$ Find how far does the car travel in the first $4,sec$. Shade the area on the graph that represents the distance travelled by the car during the period.

$(b)$ Which part of the graph represents uniform motion of the car ?