Calculate the average velocity and the speed of the minute hand of a clock.

Here are the solutions to your questions: Very Short Answer Questions: 1. Step 1: Identify the given velocities. Initial velocity u = 25 km/hour Final velocity v = 35 km/hour Step 2: Use the formula for average velocity provided in the hint. Average Velocity = Initial velocity + final velocity2 Average Velocity = 25 km/hour + 35 km/hour2 Average Velocity = 60 km/hour2 Average Velocity = 30 km/hour The average velocity of the van is 30 km/hour. 2. Step 1: Identify the given radius and time for one revolution. Radius r = 14 cm A minute hand completes one full revolution in 60 minutes. Time T = 60 minutes = 60 × 60 seconds = 3600 s Step 2: Calculate the distance covered in one revolution (circumference). Distance = 2 r = 2 × (22)/(7) × 14 cm Distance = 2 × 22 × 2 cm = 88 cm Step 3: Calculate the speed. Speed = DistanceTime = 88 cm3600 s Speed = (22)/(900) cm/s = (11)/(450) cm/s Speed ≈ 0.0244 cm/s The speed at which the tip of the minute hand moves is (11)/(450) cm/s or 0.0244 cm/s. 3. To identify whether an object is accelerating or retarding: An object is accelerating if its speed is increasing* over time, or if its velocity's direction is changing (even if speed is constant, like in circular motion). For example, a car pressing the accelerator to go faster. An object is retarding (decelerating) if its speed is decreasing* over time. For example, a car applying brakes to slow down. This can be identified by observing changes in speed using a speedometer or by measuring distances covered in equal time intervals. If distances increase, it's accelerating; if they decrease, it's retarding. 4. Two examples of uniform circular motion from daily environment: A point on the edge of a rotating fan blade: The tip of the blade moves in a circle at a constant speed, but its direction of motion continuously changes. A satellite orbiting the Earth in a circular path: The satellite maintains a constant orbital speed, but its direction of travel is always changing as it follows the curve of its orbit. In both cases, the speed (magnitude of velocity) remains constant, but the direction of the velocity vector is continuously changing. Since velocity is a vector quantity, a change in direction means a change in velocity, which implies there is an acceleration (called centripetal acceleration) acting towards the center of the circle. 5. Step 1: Convert initial and final velocities from km/h to m/s. Initial velocity u = 54 km/h = 54 × (5)/(18) m/s = 3 × 5 m/s = 15 m/s Final velocity v = 72 km/h = 72 × (5)/(18) m/s = 4 × 5 m/s = 20 m/s Time t = 10 seconds Step 2: Use the formula for acceleration. a = (v - u)/(t) a = 20 m/s - 15 m/s10 s a = 5 m/s10 s a = 0.5 m/s^2 The acceleration of the mini bus is 0.5 m/s^2. Short Answer Questions: 1. An odometer of an automobile measures the total distance travelled by the vehicle. To determine which is moving faster, we need to compare their speeds in the same units. a) Scooter moving with a speed of 300 m per minute Convert to m/s: Speed_scooter = 300 m1 minute = 300 m60 s = 5 m/s b) Car moving with a speed of 36 km per hour Convert to m/s: Speed_car = 36 km/h = 36 × 1000 m3600 s = 36 × (5)/(18) m/s = 2 × 5 m/s = 10 m/s Comparing the speeds: Scooter: 5 m/s Car: 10 m/s Since 10 m/s > 5 m/s, the car is moving faster. The car is moving faster. Last free one today — make it count tomorrow, or type /upgrade for unlimited.