Physics PDF - Velocity-Time Graphs

Fig. 7.4: Distance-time graph for a car moving with non-uniform speed The distance-time graph for the motion of the car is shown in Fig. 7.4. Note that the shape of this graph is different from the earlier distance-time graph (Fig. 7.3) for uniform motion. The nature of this graph shows nonlinear va...

Fig. 7.4: Distance-time graph for a car moving with non-uniform speed The distance-time graph for the motion of the car is shown in Fig. 7.4. Note that the shape of this graph is different from the earlier distance-time graph (Fig. 7.3) for uniform motion. The nature of this graph shows nonlinear variation of the distance travelled by the car with time. Thus, the graph shown in Fig 7.4 represents motion with non-uniform speed. 7.4.2 VELOCITY-TIME GRAPHS The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph. In this graph, time is represented along the x-axis and the velocity is represented along the y-axis. If the object moves at uniform velocity, the height of its velocity-time graph will not change with time (Fig. 7.5). It will be a straight line parallel to the x-axis. Fig. 7.5 shows the velocity-time graph for a car moving with uniform velocity of 40 km h–1. We know that the product of velocity and time give displacement of an object moving with uniform velocity. The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of the displacement. To know the distance moved by the car between time t1 and t2 using Fig. 7.5, draw perpendiculars from the points corresponding to the time t1 and t2 on the graph. The velocity of 40 km h–1 is represented by the height AC or BD and the time (t2 – t1) is represented by the length AB. So, the distance s moved by the car in time (t2 – t1) can be expressed as s = AC × CD = [(40 km h–1) × (t2 – t1) h] = 40 (t2– t1) km = area of the rectangle ABDC (shaded in Fig. 7.5). We can also study about unifor mly accelerated motion by plotting its velocity– time graph. Consider a car being driven along a straight road for testing its engine. Suppose a person sitting next to the driver records its velocity after every 5 seconds by noting the reading of the speedometer of the car. The velocity of the car, in km h–1 as well as in m s–1, at different instants of time is shown in table 7.3. Table 7.3: Velocity of a car at regular instants of time Time (s) Fig. 7.5: Velocity-time graph for uniform motion of a car 0 5 10 15 20 25 30 Velocity of the car –1 (m s–1) (km h ) 0 2.5 5.0 7.5 10.0 12.5 15.0 0 9 18 27 36 45 54 79 MOTION Rationalised 2023-24