# 4 Ways to Find Initial Speed

Velocity is a function of time and is determined by magnitude and direction. In physics problems, you often need to calculate the initial velocity (speed and direction) an object begins to move. There are several equations that can be used to determine the initial velocity. You can determine the right equation to use and answer the question using the data you know in a problem.

## Step

### Method 1 of 4: Finding Initial Velocity from Final Velocity, Acceleration, and Time

#### Step 1. Use the correct equation

To solve any physics problem, you need to know the most appropriate equation to use. Writing down all the known data is the first step to finding the right equation. If you have the final velocity, acceleration, and time values, you can use the following equation:

• Initial speed: Vi = Vf - (a*t)
• Understand what each symbol in the equation means.

• Vi is the symbol for "starting speed"
• Vf is a symbol of "final speed"
• a is the symbol for "acceleration"
• t is the symbol for "time"
• Note that this equation is the standard equation used to find the initial velocity.

#### Step 2. Fill in the known data into the equation

After writing down the known data and determining the correct equation, you can enter the values into the appropriate variables. Understanding each problem carefully, and writing down each step of the solution is important.

### If you make a mistake, you can find it easily just by going through the previous steps

#### Step 3. Solve the equation

Once all the numbers have been assigned to the appropriate variables, use the correct sequence of calculations to solve them. If allowed, use a calculator to reduce the possibility of errors in calculations.

• For example: an object moves east at an acceleration of 10 meters per second squared for 12 seconds until it reaches a final velocity of 200 meters per second. Find the object's initial velocity.

• Write down the known data:
• Vi = ?, Vf = 200 m/s, a = 10 m/s2, t = 12 s
• Multiply acceleration by time. a * t = 10 * 12 = 120
• Reduce the final speed with the above calculation results. Vi = Vf – (a * t) = 200 – 120 = 80 Vi = 80 m/s to the east.
• Write down your answer correctly. Include the unit of measurement, usually meters per second or m/s, as well as the direction in which the object is moving. Without providing information about the direction, you only provide a measure of the speed, and not the velocity of the object.

### Method 2 of 4: Finding Initial Velocity from Distance, Time, and Acceleration

#### Step 1. Use the correct equation

To solve any physics problem, you need to know which equation to use. Writing down all the known data is the first step to determining the right equation. If you know the values for distance, time, and acceleration, you can use the following equation:

• Initial speed: Vi = (d / t) - [(a * t) / 2]
• Understand what each symbol in the equation means.

• Vi is the symbol for "starting speed"
• d is the symbol for "distance"
• a is the symbol for "acceleration"
• t is the symbol for "time"

#### Step 2. Fill in the known data into the equation

After writing down all the known data and determining the correct equation, you can fill in the numbers for each of the appropriate variables. It is important to understand each question carefully and write down each calculation step.

### If you make a mistake, you can find it easily by going through the previous steps

#### Step 3. Solve the equation

After entering all the numbers into the appropriate variables, use the correct sequence of calculations to solve the problem. If allowed, use a calculator to reduce the chance of simple calculation errors.

• For example: an object is moving 150 meters west with an acceleration of 7 meters per second squared for 30 seconds. Calculate the object's initial velocity.

• Write down the known data:
• Vi = ?, d = 150 m, a = 7 m/s2, t = 30 s
• Multiply the acceleration and the time. a * t = 7 * 30 = 210
• Divide the result by 2. (a * t) / 2 = 210 / 2 = 105
• Divide the distance by time. d/t = 150/30 = 5
• Subtract the value you got in the second calculation by the value you got in the first calculation. Vi = (d / t) - [(a * t) / 2] = 5 – 105 = -100 Vi = -100 m/s to the west.
• Write down your answer correctly. Include a unit of measurement for speed, usually meters per second, or m/s, as well as the direction in which the object is moving. Without providing information about the distance, you are only providing a measure of the object's speed, not its velocity.

### Method 3 of 4: Finding Initial Velocity from Final Velocity, Acceleration, and Distance

#### Step 1. Use the correct equation

You need to know which equation to use to solve any physics problem. Writing down all the known data is the first step to determining the right equation. If you know the final velocity, acceleration, and distance in the problem, you can use the following equation:

• Initial speed: Vi = [Vf2 - (2*a*d)]
• Understand the meaning of each symbol.

• Vi is the symbol for "starting speed"
• Vf is a symbol of "final speed"
• a is the symbol for "acceleration"
• d is the symbol for "distance"

#### Step 2. Fill in the known data into the equation

After writing down all the known data and determining the correct equation, you can plug the numbers into the appropriate variables. It is important to understand each question carefully and write down each calculation step.

### If you make a mistake, you can find it easily by going through the previous steps

#### Step 3. Solve the equation

After entering all the numbers into the appropriate variables, use the correct sequence of calculations to solve the problem. If allowed, use a calculator to reduce the chance of simple calculation errors.

• For example: an object moves 10 meters north at an acceleration of 5 meters per second squared, until it reaches a final velocity of 12 meters per second. Calculate the object's initial velocity.

• Write down the known data:
• Vi = ?, Vf = 12 m/s, a = 5 m/s2, d = 10 m
• Square the final velocity. Vf2 = 122 = 144
• Multiply the acceleration by the distance and the number 2. 2 * a * d = 2 * 5 * 10 = 100
• Subtract the result of the first calculation by the result of the second calculation. Vf2 - (2 * a * d) = 144 – 100 = 44
• Root your answer. = [Vf2 - (2 * a * d)] = 44 = 6.633 Vi = 6,633 m/s to the north
• Write down your answer correctly. Include a unit of measurement for velocity, usually meters per second, or m/s, as well as the direction in which the object is moving. Without providing information about the distance, you are only providing a measure of the object's speed, not its velocity.

### Method 4 of 4: Finding Initial Velocity from Final Velocity, Time, and Distance

#### Step 1. Use the correct equation

You need to know which equation to use to solve any physics problem. Writing down all the known data is the first step to determining the right equation. If your problem includes final velocity, time, and distance, you can use the following equation:

• Initial speed: Vi = Vf + 2 (t - d)
• Understand the meaning of each symbol.

• Vi is the symbol for "starting speed"
• Vf is a symbol of "final speed"
• t is the symbol for "time"
• d is the symbol for "distance"

#### Step 2. Fill in the known data into the equation

After writing down all the known data and determining the correct equation, you can plug the numbers into the appropriate variables. It is important to understand each question carefully and write down each calculation step.

### If you make a mistake, you can find it easily by going through the previous steps

#### Step 3. Solve the equation

After entering all the numbers into the appropriate variables, use the correct sequence of calculations to solve the problem. If allowed, use a calculator to reduce the chance of simple calculation errors.

• For example: an object with a final velocity of 3 meters per second has been moving south for 45 seconds and traveled a distance of 15 meters. Calculate the object's initial velocity.

• Write down the known data:
• Vi = ?, Vf = 3 m/s, t = 15 s, d = 45 m
• Divide the distance value by time. (d/t) = (45/15) = 3
• Multiply the result by 2. 2 (d/t) = 2 (45/15) = 6
• Subtract the result of the above calculation with the final velocity. 2(d/t) - Vf = 6 - 3 = 3 Vi = 3 m/s to the south.
• Write down your answer correctly. Include a unit of measurement for velocity, usually meters per second, or m/s, as well as the direction in which the object is moving. Without providing information about the distance, you are only providing a measure of the object's speed, not its velocity.