Velocity-Time Graphs PDF

–1 Velocity (km h ) In this case, the velocity-time graph for the motion of the car is shown in Fig. 7.6. The nature of the graph shows that velocity changes by equal amounts in equal intervals of time. Thus, for all uniformly accelerated motion, the velocity-time graph is a straight line. Fig. 7.7:...

–1 Velocity (km h ) In this case, the velocity-time graph for the motion of the car is shown in Fig. 7.6. The nature of the graph shows that velocity changes by equal amounts in equal intervals of time. Thus, for all uniformly accelerated motion, the velocity-time graph is a straight line. Fig. 7.7: Velocity-time graphs of an object in nonuniformly accelerated motion. Fig. 7.6: Velocity-time graph for a car moving with uniform accelerations. You can also determine the distance moved by the car from its velocity-time graph. The area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time. If the car would have been moving with uniform velocity, the distance travelled by it would be represented by the area ABCD under the graph (Fig. 7.6). Since the magnitude of the velocity of the car is changing due to acceleration, the distance s travelled by the car will be given by the area ABCDE under the velocity-time graph (Fig. 7.6). That is, s = area ABCDE = area of the rectangle ABCD + area of the triangle ADE = AB × BC + 1 (AD × DE) 2 In the case of non-uniformly accelerated motion, velocity-time graphs can have any shape. Fig. 7.7(a) shows a velocity-time graph that represents the motion of an object whose velocity is decreasing with time while Fig. 7.7 (b) shows the velocity-time graph representing the non-uniform variation of velocity of the object with time. Try to interpret these graphs. Activity ______________ 7.9 The times of arrival and departure of a train at three stations A, B and C and the distance of stations B and C from station A are given in Table 7.4. Table 7.4: Distances of stations B and C from A and times of arrival and departure of the train Station A B C 80 Distance from A (km) 0 120 180 Time of Time of arrival departure (hours) (hours) 08:00 11:15 13:00 08:15 11:30 13:15 Plot and interpret the distance-time graph for the train assuming that its motion between any two stations is uniform. SCIENCE Rationalised 2023-24