Content

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• What you need

Velocity is a function of time and is determined by the magnitude and direction of motion. Usually in physics problems, you must calculate the initial velocity (the speed and direction of movement) of the object when it starts to move. There are many equations that can be used to calculate the initial velocity. With the information provided in the problem, you can identify the equation to use and easily find the answer.

Steps

Method 1 of 4: Find initial velocity from final velocity, acceleration and time

1. 

   Determine the correct equation to use. To solve any problem of physics, you must know which equation to use. Writing down all known information is the first step to finding the right equation. If you already have your final velocity, acceleration, and travel time, use the following equation:
   • Initial speed: V_i = V_f - (a * t)
   • Understand symbols in formulas.
     • V_i is the "initial speed"
     • V_f is the "final velocity"
     • a is "acceleration"
     • t is "time"
   • Note: this is the standard equation used when finding the initial velocity.

2. 

   
   
   Substitute the known information into the formula. After you've written down all the information you know and have identified the equations to use, you can plug in your variables. It is important that you write down each solution step carefully.
   • If you make a mistake, you can spot it easily by reviewing all previous steps.

3. 

   
   
   Solve the equation. After replacing all the known data, you should solve the problem in the correct order of calculations. If you have the permission, you should use a calculator to limit simple errors.
   • Example: An object moves east at 10 m / s, and it takes 12 seconds to reach a final speed of 200 m / s. Find the initial speed of the object.
     • Write down known information:
     • V_i = ?, V_f = 200 m / s, a = 10 m / s, t = 12 s
   • Multiply the acceleration for time. a * t = 10 * 12 =120
   • Subtract the final velocity from this product. V_i = V_f - (a * t) = 200 – 120 = 80 V_i = 80 m / s in the east.
   • Write the correct answer. Write in additional units of measure, usually in meters per second m / s, and the direction of the object's movement. If the problem does not provide direction, you will only calculate speed, not speed.
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Method 2 of 4: Find initial velocity from distance, time and acceleration

1. 

   
   
   Determine the correct equation to use. To solve any problem of physics, you must know which equation to use. Writing down all known information is the first step to finding the right equation. If you know the object's mileage, duration, and acceleration, use the following equation:
   • Initial speed: V_i = (d / t) -
   • Understand symbols in formulas.
     • V_i is the "initial speed"
     • d is "distance"
     • a is "acceleration"
     • t is "time"

2. 

   Substitute the known information into the formula. After you've written down all the information you know and have identified the equations to use, you can plug in your variables. It is important that you write down each solution step carefully.
   • If you make a mistake, you can spot it easily by reviewing all previous steps.

3. 

   Solve the equation. After replacing all the known data, you should solve the problem in the correct order of calculations. If you have the permission, you should use a calculator to limit simple errors.
   • Example: An object travels westward at an acceleration of 7 m / s and has traveled 150 m in 30 seconds. Find the initial speed of the object.
     • Write down known information:
     • V_i = ?, d = 150 m, a = 7 m / s, t = 30 s
   • Multiply the acceleration for time. a * t = 7 * 30 = 210
   • Divide the product by two. (a * t) / 2 = 210 / 2 = 105
   • Divide the distance by time. DT = 150 / 30 = 5
   • Subtract the first quotient from the first quotient. V_i = (d / t) - = 5 – 105 = -100 V_i = -100 m / s to the west.
   • Write the correct answer. Write in additional units of measure, usually in meters per second m / s, and the direction of the object's movement. If the problem does not provide direction, you will only calculate speed, not speed.
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Method 3 of 4: Find initial velocity from final speed, acceleration and distance

1. 

   Determine the correct equation to use. To solve any problem of physics, you must know which equation to use. Writing down all known information is the first step to finding the right equation. If you already have final speed, acceleration and mileage, use the following equation:
   • Initial speed: V_i = √
   • Understand symbols in formulas.
     • V_i is the "initial speed"
     • V_f is the "final velocity"
     • a is "acceleration"
     • d is "distance"

2. 

   Replace the information you already know. After you've written down all the information you know and have identified the equations to use, you can plug in your variables. It is important that you write down each solution step carefully.
   • If you make a mistake, you can spot it easily by reviewing all previous steps.

3. 

   Solve the equation. After replacing all the known data, you should solve the problem in the correct order of calculations. If you have the permission, you should use a calculator to limit simple errors.
   • Example: An object moving north at 5 m / s, has traveled 10 m, and reached a final speed of 12 m / s. Calculate the initial velocity of the object.
     • Write down known information:
     • V_i = ?, V_f = 12 m / s, a = 5 m / s, d = 10 m
   • Square the final velocity. V_f= 12 = 144
   • Multiply the acceleration for the distance and multiply by two. 2 * a * d = 2 * 5 * 10 = 100
   • Subtract this product from the square of the final velocity. V_f - (2 * a * d) = 144 – 100 = 44
   • Calculate the square root of this result. = √ = √44 = 6,633 V_i = 6,633 m / s in the north.
   • Write the correct answer. Write in additional units of measure, usually in meters per second m / s, and the direction of the object's movement. If the problem does not provide direction, you will only calculate speed, not speed.
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Method 4 of 4: Find initial velocity from final velocity, time and distance

1. 

   Determine the correct equation to use. To solve any problem of physics, you must know which equation to use. Writing down all known information is the first step to finding the right equation. If you already have your final speed, time and mileage, use the following equation:
   • Initial speed: V_i = 2 (d / t) - V_f
   • Understand symbols in formulas.
     • V_i is the "initial speed"
     • V_f is the "final velocity"
     • t is "time"
     • d is "distance"

2. 

   Substitute the known information into the formula. After you've written down all the information you know and have identified the equations to use, you can plug in your variables. It is important that you write down each solution step carefully.
   • If you make a mistake, you can spot it easily by reviewing all previous steps.

3. 

   Solve the equation. After replacing all the known data, you should solve the problem in the correct order of calculations. If you have the permission, you should use a calculator to limit simple errors.
   • Solve the equation. After replacing all the known data, you should solve the problem in the correct order of calculations. If you have the permission, you should use a calculator to limit simple errors.
     • Write down known information:
     • V_i = ?, V_f = 3 m / s, t = 15 s, d = 45 m
   • Divide the distance by time. (DT) = (45/15) = 3
   • Multiply that value by 2. 2 (d / t) = 2 (45/15) = 6
   • Subtract the product from the final velocity. 2 (d / t) - V_f = 6 - 3 = 3 V_i = 3 m / s to the south.
   • Write the correct answer. Write in additional units of measure, usually in meters per second m / s, and the direction of the object's movement. If the problem does not provide direction, you will only calculate speed, not speed.
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What you need

• Pencil
• Paper
• Handheld computer (optional)