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Q 10.     An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

Given, Radius of the circular orbit =   Circumference of the orbit =  The satellite takes 24 hours to revolve around the earth. We know,  Therefore, the speed of the artificial satellite is 

Q 9.     State which of the following situations are possible and give an example for each of these:

    (c)     an object moving in a certain direction with an acceleration in the perpendicular direction.

(c) The given situation is possible. For an object moving in a circular path with constant speed, the direction of its velocity at any point will be tangential to that point. However, its acceleration will be directed radially inwards. (Constant speed but still having an acceleration - Due to continuous change in direction.) 

Q 9.        State which of the following situations are possible and give an example for each of these: 

     (b)     an object moving with an acceleration but with uniform speed. 

(b) The given situation is possible.  An object moving in a circular path with uniform speed, i.e covering equal distance in equal amount of time is still under acceleration. Because, the velocity keeps on changing due to continuous change in the direction of motion. Therefore, circular motion is an example of an object moving with an acceleration but with uniform speed. 

Q 9.     State which of the following situations are possible and give an example for each of these:

          (a)     an object with a constant acceleration but with zero velocity 

(a) The given situation is possible. When an object is thrown upwards (under gravity only), it reaches to a maximum height where its velocity becomes zero. However, it still has an acceleration acting in the downward direction (acceleration due to gravity). Note: This is possible for a given point of time, however, it is not possible for a period of time. 

Q 8.     The speed-time graph for a car is shown is Figure:

             

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

In uniform motion, the speed of car will become constant which is represented by line parallel to the time axis. In the given figure, the straight line graph from  represents the uniform motion of the car. 

Q 8.     The speed-time graph for a car is shown is Figure:

             

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

Given is a speed-time graph. The area under the curve will give the distance travelled by the car. In time , the distance travelled by the car will be equal to the area under the curve from  Considering this part of the graph as a quarter of a circle whose radius = 4 unit. Therefore, required area =  Therefore, distance the car travelled in the first 4 seconds is 

Q 7.     A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground?  After what time will it strike the ground?

Considering downward direction as positive direction. Given, Height from which ball is dropped,  Acceleration of the ball,  =  Initial velocity,  (i) We know,  (In downward direction) Therefore, the ball will strike the ground with a velocity of  (ii) Now, we know,  Therefore, the ball reaches the ground in . Note:  was rejected because in this case, the negative sign implies the velocity in...

Q 6.     Figure shows the distance-time graph of three objects A,B and C. Study the graph and answer the following questions:

            

    (d)     How far has B travelled by the time it passes C?

Given is a distance-time graph. The graph of B and C intersect at a point whose y-coordinate is 5. Hence, B has travelled by the time it passes C.

Q 6.     Figure shows the distance-time graph of three objects A,B and C. Study the graph and answer the following questions:

            

  (c)     How far has C travelled when B passes A?

Given is a distance-time graph. Any point on the curve will give the distance of object from O. To find how far C has travelled when B passes A, draw a perpendicular from the intersection point of A and B on time axis. The point where it intersects on the C graph, from C draw a perpandicular to y axis . Therefore, distance travelled by C will be (Final distance from O - Initial distance from...

Q 6.     Figure shows the distance-time graph of three objects A,B and C. Study the graph and answer the following questions:

            

    (b)     Are all three ever at the same point on the road?

Given is a distance-time graph. Any point on the curve will give the distance of object from O. Since there is no intersection point of all the three graphs, they never meet at the same point on the road.  (Although any two of them do meet at some point on the road!) 

Q 6.     Figure shows the distance-time graph of three objects A,B and C. Study the graph and answer the following questions:

            

    (a)     Which of the three is travelling the fastest?

Given is a distance-time graph. The slope of this graph gives us speed. Hence, the graph with the highest slope will have the highest speed. Since B has the highest slope(inclination), it travels the fastest.

Q 5.     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?

The initial speed   After 5 sec the car stops The graph is represented by the blue line ( x-axis is time and the y-axis is speed)  For the car with 3Kmh-1. Initial speed   .  The graph which is represented by the golden line The area covered by the blue graph is greater than the golden graph so the car with 15 m/s initial velocity travells large distance.

Q 4.     A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0\ m s^{-2} for 8.0 s. How far does the boat travel during this time?

Given, The motorboat starts from rest. Hence, initial speed of the motorboat, u =  Acceleration of the motorboat,  =  Time taken,  (b) We know,  Therefore, the distance travelled by the motorboat is 

Q 3.     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 30\ km h^{-1}. What is the average speed for Abdul’s trip?

Given, Average speed while going to school,  And Average speed while returning back from school,  Let the distance between starting point and school be  And time taken by Abdul during the two trips be  We know,  And,              -(i) Now, Total distance that Abdul covers =  And total time Abdul takes to cover this distance = Therefore, the average speed for Abdul's trip is  (Note: )

Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging

             (a) from A to B and

              (b) from A to C?

Given, (a) Distance between A and B = Time taken to reach from A to B =    Average speed from A to B =  And, Average velocity from A to B =  (In this case, average speed is equal to the average velocity) (b) Distance travelled from A to reach C =   And, Displacement from A to C =  Also, time taken to reach C from A =   Average speed from A to C =  And, Average velocity from A to C =  (In this...

Q 1.     An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

Given, Diameter of the circular track =  The circumference of the circular track,   The athlete completes one round of a circular track in 40 s.  Speed of the athlete =  In , Distance travelled by the athlete =  Also, number of rounds the athlete will complete in  =  Therefore, the final position of the athlete after  will be diametrically opposite to his initial point. (3 complete rounds and...

Q 5.     A stone is thrown in a vertically upward direction with a velocity of 5\ m s^{-1}. If the acceleration of the stone during its motion is 10\ m s^{-2} in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Taking upward direction as positive (+) direction: Given,          (This is due to gravitational force!) The stone will move up until its velocity becomes zero. We know,  Therefore, the stone reaches to a height of  Now,  We know,  Therefore, the time taken by the stone to reach the maximum height is .    

 A racing car has a uniform acceleration of 4 m s-2. What distance will it cover in 10 s after start?

Given, Initial speed of the racing car, u =  Acceleration of the car,  =  Time taken,  We know,  Therefore, the distance travelled by the racing car in  is 

 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 the train will go before it is brought to rest.

(We know, ) Given, Initial speed of the train,  =  Acceleration of the train,   (Negative sign implies retardation) Since, the train has to be brought to rest, final speed of the train,  =  We know,  Therefore, the train travels a distance of  before coming to rest.

A trolley, while going down an inclined plane, has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start?

Given, The trolley starts from rest. Hence, the initial speed of the trolley, =  Acceleration of the trolley,  =  Time is taken,  (a) We know,  Therefore, the velocity of the trolley after 3 sec is 
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