Physics PDF - Average Speed & Velocity

Look at the situations given in Fig. 7.2. If the bowling speed is 143 km h–1 in Fig. 7.2(a) what does it mean? What do you understand from the signboard in Fig. 7.2(b)? Different objects may take different amounts of time to cover a given distance. Some of them move fast and some move slowly. The ra...

Look at the situations given in Fig. 7.2. If the bowling speed is 143 km h–1 in Fig. 7.2(a) what does it mean? What do you understand from the signboard in Fig. 7.2(b)? Different objects may take different amounts of time to cover a given distance. Some of them move fast and some move slowly. The rate at which objects move can be different. Also, different objects can move at the same rate. One of the ways of measuring the rate of motion of an object is to find out the distance travelled by the object in unit time. This quantity is referred to as speed. The SI unit of speed is metre per second. This is represented by the symbol m s–1 or m/s. The other units of speed include centimetre per second (cm s–1) and kilometre per hour (km h–1). To specify the speed of an object, we require only its magnitude. The speed of an object need not be constant. In most cases, objects will be in non-uniform motion. Therefore, we describe the rate of motion of such objects in terms of their average speed. The average speed of an object is obtained by dividing the total distance travelled by the total time taken. That is, average speed = Total distance travelled Total time taken If an object travels a distance s in time t then its speed v is, v= s t (7.1) Let us understand this by an example. A car travels a distance of 100 km in 2 h. Its average speed is 50 km h–1. The car might not have travelled at 50 km h–1 all the time. Sometimes it might have travelled faster and sometimes slower than this. Example 7.1 An object travels 16 m in 4 s and then another 16 m in 2 s. What is the average speed of the object? Average speed = = Total distance travelled Total time taken 32 m –1 6 s = 5.33 m s Therefore, the average speed of the object is 5.33 m s–1. 7.2.1 SPEED WITH DIRECTION The rate of motion of an object can be more comprehensive if we specify its direction of motion along with its speed. The quantity that specifies both these aspects is called velocity. Velocity is the speed of an object moving in a definite direction. The velocity of an object can be uniform or variable. It can be changed by changing the object’s speed, direction of motion or both. When an object is moving along a straight line at a variable speed, we can express the magnitude of its rate of motion in terms of average velocity. It is calculated in the same way as we calculate average speed. In case the velocity of the object is changing at a uniform rate, then average velocity is given by the arithmetic mean of initial velocity and final velocity for a given period of time. That is, average velocity = initial velocity + final velocity 2 u+v Mathematically, v av = 2 (7.2) where vav is the average velocity, u is the initial velocity and v is the final velocity of the object. Speed and velocity have the same units, that is, m s–1 or m/s. Activity ______________ 7.6 Solution: Total distance travelled by the object = 16 m + 16 m = 32 m Total time taken = 4 s + 2 s = 6 s Measure the time it takes you to walk from your house to your bus stop or the school. If you consider that your average walking speed is 4 km h–1, estimate the distance of the bus stop or school from your house. 75 MOTION Rationalised 2023-24