Question 53:
The graph given alongside shows the positions of a body at different times. Calculate the speed of the body as it moves from :
(i) A to B,
(ii) B to C, and
(iii) C to D.
Solution :
(i) The distance covered from A to B is( 30) =3 cm
Time taken to cover the distance from A to B =(5 2) =3s
(ii) The speed of the body as it moves from B to C is zero.
(iii) The distance covered from C to D is (73)=4 cm
Time taken to cover the distance from C to D = (97)=2s
Question 54:
What can you say about the motion of a body if:
(a) its displacementtime graph is a straight line ?
(b) its velocitytime graph is a straight line ?
Solution :
(a) The body has a uniform velocity if its displacementtime graph is a straight line.
(b) The body has a uniform acceleration if its velocitytime graph is a straight line.
Question 55:
A body with an initial velocity x moves with a uniform acceleration y. Plot its velocitytime graph.
Solution :
Question 56:
Given alongside is the velocitytime graph for a moving body :
Find :
(i) Velocity of the body at point C.
(ii) Acceleration acting on the body between A and
(iii) Acceleration acting on the body between B and C.
Solution :
(i) BC represents uniform velocity. From graph, we see that the velocity of the body at point C = 40km/h
(ii) Acceleration between A and B = slope of line AB
(iii) BC represents uniform velocity, so acceleration acting on the body between B and C is zero.
Question 57:
A body is moving uniformly in a straight line with a velocity of 5 m/s. Find graphically the distance covered by it in 5 seconds.
Solution :
Distance travelled = Area of rectangle OABC
= OA x OC
= 5 x 5 =25 m
Question 58:
The speedtime graph of an ascending passenger lift is given alongside.
What is the acceleration of the lift:
(i) during the first two seconds ?
(ii) between second and tenth second ?
(iii) during the last two seconds ?
Solution:
(i) Acceleration during first two seconds
(ii) Acceleration between second and tenth second is zero, since the velocity is constant during this time.
(iii) Acceleration during last two seconds
Question 59:
A car is moving on a straight road with uniform acceleration. The speed of the car varies with time as follows :
Draw the speedtime graph by choosing a convenient scale. From this graph :
(i) Calculate the acceleration of the car.
(ii) Calculate the distance travelled by the car in 10 seconds.
Solution :
(i) Acceleration of the car = slope of line AB
(ii) Distance travelled by the car in 10 s = area of trapezium OABC
Question 60:
The graph given alongside shows how the speed of a car changes with time:
(i) What is the initial speed of the car ?
(ii) What is the maximum speed attained by the car ?
(iii) Which part of the graph shows zero acceleration ?
(iv) Which part of the graph shows varying retardation ?
(v) Find the distance travelled in first 8 hours.
Solution :
(i) Initial speed of the car=10km/h
(ii) Maximum speed attained by the car= 35km/h
(iii) BC represents zero acceleration.
(iv) CD represents varying retardation.
(v)
Distance travelled in first 8 hrs:
s= Area of trapezium OABF + Area of rectangle BCEF
Question 61:
Three speedtime graphs are given below :
Which graph represents the case of:
(i) a cricket ball thrown vertically upwards and returning to the hands of the thrower ?
(ii) a trolley decelerating to a constant speed and then accelerating uniformly ?
Solution :
(i) Graph (c): The speedof the ball goes on decreasing uniformly as it moves upward, reaches zero at the highest point, and then increases uniformly as it moves downward.
(ii) Grap(a): The speed of the trolley decreases uniformly, then it moves at a constant speed, and then the speed increases uniformly.
1 videos228 docs21 tests

1. What is motion? 
2. What are the different types of motion? 
3. What is the difference between speed and velocity? 
4. What is the formula to calculate speed? 
5. What is acceleration? 
1 videos228 docs21 tests


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