SAT Physics Subject Test

Chapter 2 Kinematics

ACCELERATION

When you step on the gas pedal in your car, the car’s speed increases; step on the brake and the car’s speed decreases. Turn the wheel, and the car’s direction of motion changes. In all of these cases, the velocity changes. To describe this change in velocity, we need a new term: acceleration. In the same way that velocity measures the rate of change of an object’s position, acceleration measures the rate of change of an object’s velocity. An object’s average acceleration is defined as follows:


average acceleration = 


The units of acceleration are meters per second, per second: [a] = m/s2. Because ∆v is a vector, ā is also a vector; and because ∆t is a positive scalar, the direction of ā is the same as the direction of ∆v.

Furthermore, if an object’s original direction of motion is positive, then an increase in speed corresponds to a positive acceleration, while a decrease in speed corresponds to a negative acceleration (deceleration).

Notice that an object can accelerate even if its speed doesn’t change. (Again, don’t let the everyday usage of the word accelerate confuse you!) This is because acceleration depends on ∆v, and the velocity vector v changes if (1) speed changes, (2) direction changes, or (3) both speed and direction change. For instance, a car traveling around a circular racetrack is continuously accelerating even if the car’s speed is constant because the direction of the car’s velocity vector is constantly changing.

  5. A car is traveling in a straight line along a highway at a constant speed of 80 miles per hour for 10 seconds. Find its acceleration.

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Since the car is traveling at a constant velocity, its acceleration is zero. If there’s no change in velocity, then there’s no acceleration.

  6. A car is traveling in a straight line along a highway at a speed of 20 m/s. The driver steps on the gas pedal and, 3 seconds later, the car’s speed is 32 m/s. Find its average acceleration.

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Assuming that the direction of the velocity doesn’t change, it’s simply a matter of dividing the change in velocity, 32 m/s – 20 m/s = 12 m/s, by the time interval during which the change occurred: ā = ∆v/∆t = (12 m/s) / (3 s) = 4 m/s2.

  7. Spotting a police car ahead, the driver of the car in the previous example slows from 32 m/s to 20 m/s in 2 sec. Find the car’s average acceleration.

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Dividing the change in velocity, 20 m/s – 32 m/s = –12 m/s, by the time interval during which the change occurred, 2 s, gives us ā = ∆v/∆t = (–12 m/s) / (2 s) = –6 m/s2. The negative sign means that the direction of the acceleration is opposite the direction of the velocity: The car is slowing down.

If an object has negative velocity, then a positive acceleration means it is slowing down and a negative acceleration means it is speeding up. This can be confusing. Just remember that if velocity and acceleration point in the same direction, the object is speeding up and if they point in opposite directions, it is slowing down.

Note: If velocity and acceleration are perpendicular, the object is turning with constant speed.


The Skinny on Acceleration

Since acceleration is defined as the change in velocity per change in time, we can say the following:

If a is in the same direction as v, then the object is speeding up.

If a is in the opposite direction as v, then the object is slowing down.

If a = 0 in the direction of v, the object’s speed is not changing (though its velocity may be, if there is acceleration perpendicular to the velocity).

This means that, for example, positive acceleration does not necessarily imply that an object is speeding up. If the velocity is negative, positive acceleration means that the velocity is becoming less negative (slowing down).


We will discuss this further in Chapter 3.