Content

• Steps
• Method 1 of 2: Calculating Average Acceleration
• Method 2 of 2: Positive and negative acceleration
• Tips

Acceleration characterizes the rate of change in speed both in magnitude and in direction. Average acceleration can be found to determine the average rate of change in body speed over a period of time. You may not know how to calculate acceleration (since this is not a routine task), but with the right approach, it shouldn't be difficult.

Steps

Method 1 of 2: Calculating Average Acceleration

1. 1 Determination of acceleration. Acceleration is the rate at which speed increases or decreases, or simply the rate at which speed changes over time. Acceleration is a vector quantity with a direction (include it in the answer).
   • Usually, if the body accelerates while moving "to the right", "up" or "forward", then the acceleration has a positive (+) value.
   • If the body accelerates when moving "to the left", "down" or "back", then the acceleration has a negative (+) value.
2. 2 Write down the definition of acceleration as a formula. As mentioned above, acceleration is the rate at which speed changes over time. There are two ways to write this definition as a formula:
   • a_Wed = /_Δt (the delta symbol "Δ" means "change").
   • a_Wed = /_{(tTo - tn)}where v_To - final speed, v_n - starting speed.
3. 3 Find the starting and ending velocities of the body. For example, a car starting movement (to the right) from a parking lot has an initial speed of 0 m / s, and a final speed of 500 m / s.
   • The movement to the right is described by positive values, so further we will not indicate the direction of movement.
   • If the vehicle starts moving forward and ends up moving backward, the final speed is negative.
4. 4 Note the change in time. For example, it may take a car 10 seconds to reach its final speed. In this case t_To = 10 s, and t_n = 0 s.
   • Make sure the speed and time are in the correct units. For example, if the speed is given in km / h, then the time should be measured in hours.
5. 5 Plug your speed and time data into the formula to calculate the average acceleration. In our example:
   • a_Wed = /_{(10s - 0s)}
   • a_Wed = /_(10s)
   • a_Wed = 50 m / s / s, that is, 50 m / s.
6. 6 Interpretation of the result. Average acceleration sets the average rate of change in speed over a specified period of time. In the example above, the car accelerated on average 50 m / s per second. Remember: the motion parameters can be different, but the average acceleration will be the same only if the speed change and time change do not change:
   • The car can start moving at a speed of 0 m / s and accelerate in 10 seconds to 500 m / s.
   • The car can start moving at a speed of 0 m / s and accelerate to 900 m / s, and then slow down to 500 m / s in 10 seconds.
   • The car can start moving at a speed of 0 m / s, stand still for 9 seconds, and then accelerate to 500 m / s in 1 second.

Method 2 of 2: Positive and negative acceleration

1. 1 Determination of positive and negative speed. Velocity has a direction (since it is a vector quantity), but specifying it, for example, as "up" or "north" is very tedious. Instead, most problems assume that the body is moving along a straight line.When moving in one direction, the speed of the body is positive, and when moving in the opposite direction, the speed of the body is negative.
   • For example, a blue train is heading east at a speed of 500 m / s. The red train moves westward at the same speed, but since it is moving in the opposite direction, its speed is recorded as -500 m / s.
2. 2 Use the definition of acceleration to determine its sign (+ or -). Acceleration is the rate at which speed changes over time. If you do not know what sign to write at the acceleration value, find the change in speed:
   • v_{the ultimate} - v_initial = + or -?
3. 3 Acceleration in different directions. For example, blue and red trains are moving in opposite directions at a speed of 5 m / s. Imagine this movement on the number line; the blue train moves at a speed of 5 m / s in the positive direction of the number line (i.e. to the right), and the red train moves at a speed of -5 m / s in the negative direction of the number line (i.e. to the left). If each train increases its speed by 2 m / s (in the direction of its movement), what is the acceleration sign? Let's check:
   • The blue train is moving in a positive direction, so its speed increases from 5 m / s to 7 m / s. The final speed is 7 - 5 = +2. Since the change in speed is positive, the acceleration is also positive.
   • The red train moves in a negative direction and increases its speed from -5 m / s to -7 m / s. The final speed is -7 - (-5) = -7 + 5 = -2 m / s. Since the change in speed is negative, then the acceleration is also negative.
4. 4 Slowdown. For example, an airplane flies at 500 km / h and then decelerates to 400 km / h. Although the plane is moving in a positive direction, its acceleration is negative as it slows down (that is, decreases speed). This can be checked through calculations: 400 - 500 = -100, that is, the change in speed is negative, therefore the acceleration is negative.
   • On the other hand, if the helicopter moves at a speed of -100 km / h and accelerates to -50 km / h, then its acceleration is positive, because the change in speed is positive: -50 - (-100) = 50 (although such a change in speed was not enough to change the direction of the helicopter).

Tips

Acceleration and velocity are vector quantities that are specified by both value and direction. Values ​​specified only by value are called scalar (for example, length).