3 Acceleration BEFORE YOU READ Describe what happens to the speed of a bicycle as it goes uphill and downhill. WHAT YOU’LL LEARN • how acceleration, time, and velocity are related • the three ways an object can accelerate • how to calculate acceleration • the similarities and differences between straight line motion, circular motion, and projectile motion READ TO LEARN Copyright © McGraw-Hill Education Velocity and Acceleration A car sitting at a stoplight is not moving. When the light turns green, the driver presses the gas pedal and the car starts moving. The car moves faster and faster. Speed is the rate of change of position. Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Remember that velocity is a measure that includes both speed and direction. Because of this, a change in velocity can be either a change in how fast something is moving or a change in the direction it is moving. Acceleration means that an object changes its speed, its direction, or both. When you think of acceleration, you might think of speeding up. But an object that is slowing down also is accelerating. An object that is changing direction is accelerating, too. Like velocity and momentum, acceleration has a direction. The figure below shows the three ways an object can accelerate. When the car is speeding up, its acceleration and velocity are in the same direction. When the car is slowing down, its acceleration is in the opposite direction of its velocity. When the car changes direction, the acceleration is not in the same direction or opposite direction as the car’s velocity. Speeding Up Acceleration Velocity Slowing Down STUDY COACH Outlining As you read the lesson, make an outline of the important information in each paragraph. Get It? 1. Identify three ways that an object can accelerate. Changing Direction Acceleration Velocity Velocity Acceleration Reading Essentials • Motion 33 Speed of Tamara’s Car Moving at a constant speed 25 Speed (km/h) 20 Slowing down to enter parking lot Speeding up 15 Slowing down at a red light 10 5 Pulling out of driveway 0 1 Parking Stopped at red light 2 3 4 5 6 7 Time (min) Speed-time graphs and acceleration When an object travels in a straight line and does not change M02_023A-668304 direction, a graph of speed versus time can provide information Venn Diagram about an object’s acceleration. Look at the speed-time graph Make the following trifold above of Tamara’s car as she drives to the store. Remember that Foldable to compare and the slope of a line on a distance-time graph is the object’s speed. contrast the characteristics of acceleration, speed, and The slope of a line on a speed-time graph is the object’s velocity. acceleration. For example, when Tamara pulls out of her driveway, the car’s acceleration is 0.33 km/min2, which is equal to Acceleration the slope of the line from t = 0 to t = 0.5 min. D Construct a Speed Velocity APPLYING MATH Acceleration is the rate of change in velocity. To calculate acceleration, divide the change in velocity by the time interval over which the change happened. The change in velocity is the final velocity minus the initial velocity. If the object moves in a straight line, the size of the change in velocity can be calculated from the change in speed. Then, the acceleration of an object can be calculated from the following equation. acceleration (a) = APPLYING MATH 3. Calculate Suppose a bird takes off from a tree and flies in a straight line. It reaches a speed of 10 m/s. What is the change in the bird’s velocity? vf - vi change in velocity (v) _____ or a = t time (t) In SI units, velocity has units of m/s and time has units of s, so the SI unit of acceleration is m/s2. In some cases, your calculations will result in a negative acceleration. The negative sign means in the opposite direction. For example, an acceleration of −10 m/s2 north is the same as 10 m/s2 south. Reading Essentials • Motion 34 Copyright © McGraw-Hill Education 2. Use Variables Write what M02_005A-685545 vf and vi mean. Calculating acceleration Motion in Two Dimensions So far, we have only discussed motion in a straight line. But most objects don’t move only in a straight line. Recall that we cannot add measurements that are not in the same or opposite directions. So, we will discuss motion in each direction separately. For example, suppose a student walked three blocks north and four blocks east. You could say the student walked north for three blocks at 1 m/s and then walked east for four blocks at 2 m/s. Recall that objects that change direction are accelerating. For an object that is changing direction, its acceleration is not in the same or opposite direction as its velocity. This means that we cannot use the acceleration equation. Just as with displacement and velocity, accelerations that are not in the same or opposite directions cannot be directly combined. Get It? 4. Explain why you cannot use the acceleration equation for an object that changes direction. APPLYING MATH 5. Explain Why is the acceleration of an object moving at a constant velocity always 0? Circular motion Think about a horse’s horizontal motion on a carousel. The horse moves in a circular path. Its speed remains constant, but the horse is accelerating. That is because its direction of motion changes. The change in the direction of the horse’s velocity is toward the center of the carousel. The horse’s velocity is perpendicular to the inward acceleration. Acceleration toward the center of a curved or circular path is called centripetal acceleration. In the same way, Earth experiences centripetal acceleration as it orbits the Sun in a nearly circular path. Copyright © McGraw-Hill Education Projectile motion If you have tossed a ball to someone, you have probably noticed that thrown objects do not travel in straight lines. They curve downward. That is why quarterbacks, dart players, and archers aim above their targets. Anything that is thrown or shot through the air is called a projectile. Earth’s gravity causes projectiles to follow a curved path. When you throw or shoot an object, like a ball or rubber band, the force exerted gives the object a horizontal velocity. The horizontal velocity is constant. The rubber band does not accelerate horizontally. If there were no gravity, the rubber band would move along a straight line. However, when you release a rubber band, gravity causes it to accelerate downward. The rubber band has an increasing vertical velocity. The result of these two motions is that the rubber band travels in a curve, even though its horizontal and vertical motions are completely independent of each other. Reading Essentials • Motion 35 Get It? 6. Define the term centripetal acceleration. If you were to throw a ball as hard as you could in a perfectly horizontal direction, would it take longer to reach the ground than if you dropped a ball from the same height? Surprisingly, it will not. A thrown ball and a dropped ball will hit the ground at the same time. Both balls travel the same vertical distance in the same amount of time. However, the ball thrown horizontally travels a greater horizontal distance than the ball that is dropped. THINK IT OVER 7. Think Critically A car that is slowing down is still moving forward. Why is this considered negative acceleration? Amusement park acceleration Riding roller coasters in amusement parks can give you the feeling of danger, but these rides are designed to be safe. Engineers use the laws of physics to design amusement park rides that are thrilling but harmless. Roller coasters are constructed of steel or wood. Because wood is not as strong as steel, wooden roller coasters do not have hills that are as high and as steep as some steel roller coasters have. The highest speeds and accelerations are usually produced on steel roller coasters. Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations. As riders move down a steep hill or an inversion loop, they will accelerate toward the ground due to gravity. When riders go around a sharp turn, they are also accelerated. This acceleration makes them feel as if a force is pushing them toward the side of the car. Copyright © McGraw-Hill Education Reading Essentials • Motion 36
