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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 

 A bus starting from rest moves with a uniform acceleration of 0.1 m s-2 for 2 minutes. Find

             (b) the distance travelled.

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

  A bus starting from rest moves with a uniform acceleration of 0.1 m s-2 for 2 minutes. Find

             (a) the speed acquired

Given, The bus starts from rest. Hence, the initial speed of the bus =  Acceleration of the bus,  =  Time is taken,  (a) We know,  Therefore, the speed acquired by the bus is 

What is the quantity which is measured by the area occupied below the velocity-time graph?

The area occupied below the velocity-time graph denotes the total distance travelled by an object in the given time frame. We know,  

What can you say about the motion of an object if its speedtime graph is a straight line parallel to the time axis?

If the speed-time graph of an object is a straight line parallel to the time axis, it means that the speed of the object is not changing with time. Hence the speed of the object is constant. This also implies that the acceleration of the object is zero.

What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

If the distance-time graph of an object is a straight line parallel to the time axis, it means that the distance of the object is the same from its initial position at any point of time. This implies that the object is not moving and is at rest.

  What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?

Distance-time graph is the plot of distance travelled by an object along x-axis against time along y-axis. For the uniform motion of an object, the distance-time graph is a straight line with a constant slope. (Note: However, the path may be straight or curved!) For non-uniform motion of an object, the distance-time graph is a curved line with an increasing or decreasing slope.

 A train starting from a railway station and moving with uniform acceleration attains a speed 40 km h-1 in 10 minutes. Find its acceleration.

(We know, ) Given, The train starts from rest. Hence, the initial speed of the train =  Final speed of the train =  Time taken,  We know,  Therefore, the acceleration of the train is  

A bus decreases its speed from 80 km h-1 to 60 km h-1 in 5 s. Find the acceleration of the bus.

(We know, ) Given, Initial speed of the bus,  =  The final speed of the bus, =  Time is taken,   We know,  The negative sign implies retardation. Therefore, the acceleration of the bus is  Or, the retardation(de-acceleration) of the bus is 

         When will you say a body is in

           (i) uniform acceleration?

            (ii) nonuniform acceleration?

(i) If the velocity of an object travelling in a straight line increases or decreases by equal amounts in equal intervals of time, then the acceleration of the object is said to be uniform. For example, An apple having a free-fall motion. (ii) On the other hand, if the velocity of the object increases or decreases by unequal amounts in equal intervals of time, then the acceleration of the...

 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}ms^{-1}.

Given, the signal travels at the speed of light,  . Time taken by the signal = Let the distance of the spaceship from the ground station be  We know,  Therefore, the distance of spaceship from the ground station is  

     What does the path of an object look like when it is in uniform motion?

An object is having a uniform motion if it covers equal distance in equal interval of time (which implies speed is constant!). So the path can be straight or curved. For eg. Consider a circular path. For understanding purposes, divide the circumference of the circle in six equal parts each subtending  at the centre. The object covers each equal part in equal amount of time. Hence, by...

    What does the odometer of an automobile measure?

Odometer is a device which measures the total distance travelled by automobile. 

Q 1.     An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

Yes, an object having moved through a distance can have zero displacement.  If an object moves and returns to the original position, the displacement will be zero. Consider the movement in a circular path. A man walks from point A in a circular path in a park and comes back to the point A. The distance travelled is equal to the circumference of the circular path, but displacement is zero.
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