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.
(i) The distance covered from A to B is( 3-0) =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 (7-3)=4 cm
Time taken to cover the distance from C to D = (9-7)=2s
What can you say about the motion of a body if:
(a) its displacement-time graph is a straight line ?
(b) its velocity-time graph is a straight line ?
(a) The body has a uniform velocity if its displacement-time graph is a straight line.
(b) The body has a uniform acceleration if its velocity-time graph is a straight line.
A body with an initial velocity x moves with a uniform acceleration y. Plot its velocity-time graph.
Given alongside is the velocity-time graph for a moving body :
(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.
(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.
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.
Distance travelled = Area of rectangle OABC
= OA x OC
= 5 x 5 =25 m
The speed-time 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 ?
(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
A car is moving on a straight road with uniform acceleration. The speed of the car varies with time as follows :
Draw the speed-time 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.
(i) Acceleration of the car = slope of line AB
(ii) Distance travelled by the car in 10 s = area of trapezium OABC
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.
(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.
Distance travelled in first 8 hrs:
s= Area of trapezium OABF + Area of rectangle BCEF
Three speed-time 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 ?
(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. 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?|