Acceleration Speed Distance Calculator

An online calculator for calculating acceleration, speed and distance for uniformly accelerated, rectilinear motion calculates and givess a detailed step-by-step solution.

The calculator calculates:
Calculator for calculating the acceleration at a straight line uniformly accelerated motion.
Calculator for calculating the final speed at the end of a period of time with uniformly accelerated rectilinear motion.
Calculator for calculating the initial speed at time t0 with uniformly accelerated rectilinear motion.
Object displacement calculator for rectilinear uniformly accelerated motion.
Examples of calculating acceleration, speed and distance.

Contents:

Decimal.
Fraction a/b.
Product of numbers a*b.

Pi (π).
Euler's number e.
E is a letter meaning 10ⁿ.

Square root Sqrt(x).
Root of any degree Root(n, x).
Exponentiation Pow(n, x).

Logarithm Log(n, x).
Natural logarithm Ln(n).
Common logarithm Lg(n).
Binary logarithm Lb(n).

Greatest common divisor Gcd(n, m).
Least common multiple Lcm(n, m).

Trigonometric functions.
Sine of an angle Sin(x).
Cosine of an angle Cos(x).
Tangent of an angle Tan(x).
Cotangent of an angle Cot(x).
Secant of an angle Sec(x).
Cosecant of an angle Csc(x).

Inverse trigonometric functions.
Arcsine Asin(x).
Arccosine Acos(x).
Arctangent Atan(x).
Arccotangent Acot(x).
Arcsecant Asec(x).
Arcsecant Acsc(x).

Expressions containing multiple embedding of functions and mathematical operations.

Decimal

Notation:
Use a point or a comma to write a fraction

Examples:
1.12 or 1,12

Fraction a/b

Notation:
To enter fractions, use the sign «/»

Examples:
1/2 or 3/4

Product of numbers

Notation:
To write the product of two numbers, use the sign «*»

Examples:
5*4

Pi (π)

Notation:
To write the number π, enter «π», or «pi».

Examples:
Sin(π)

Euler's number e
e = 2.7182818284...

Notation:
To write the number e enter e or E.

Examples:
Cos(e)

E is a letter meaning 10ⁿ

Notation:
The letter E should only be in the number

Examples:
16e+6
16e-4
3.96e+3

Square root Sqrt(x)

Notation:
Sqrt(x), where
x – any non-negative number or expression.

Examples:
Sqrt(3)
Sqrt(3/5)
Sqrt(3*3)

Root of any degree Root(n, x)

Notation:
Root(n, x), where
n – redicand
x – index
x, n – any numbers or expressions.
For an even root, the redicand cannot be negative.

Examples:
Cubic root of fraction 2/5
Root(2/5, 3)

Other examples
Root(1.5, 3)
Root((3*5), 3/2)
Root(1.5, 3/7)

Exponentiation Pow(n, x)

Notation:
Pow(n, x), where
n – base
x – exponent or power
x, n – any numbers or expressions.

Examples:
Five to the power of three
Pow(5, 3)

Other examples
Pow(12.5, 3)
Pow((3-5), 3/2)
Pow(1.5, Sqrt(2))

Logarithm Log(n, x)

Notation:
Log(n, x), where
n – the number whose logarithm you want to find
x – base.
x > 0, x ≠ 1, n > 0

Examples:
Log5 34 (logarithm of 34 to base 5), should be written as
Log(34, 5)

Natural logarithm Ln(n)
The base is equal to Euler's number e
(e = 2.7182818284...)

Notation:
Ln(n), where
n > 0<

Examples:
Ln(7)

Common logarithm Lg(n)
The logarithm base 10

Notation:
Lg(n), where
n > 0

Examples:
Lg(1.6)

Binary logarithm Lb(n)
The logarithm base 2

Notation:
Lb(n), where
n > 0

Examples:
Lb(3/6)

Greatest common divisor Gcd(n, m)

Notation:
Gcd(n, m), where
n, m – non-negative integers

Examples:
Gcd(12; 16) should be written as
Gcd(12, 16)

Least common multiple Lcm(n, m)

Notation:
Lcm(n, m), where
n, m – non-negative integers

Examples:
Lcm(4; 23) should be written as
Lcm (4, 23)

Trigonometric functions
All trigonometric functions take one or two arguments. If the function takes one argument, then the number is considered to be in radians.

Sine of an angle Sin(x)

Notation:
Sin(x)
Sin(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Sine π/3 radians
Sin(π/3) or Sin(π/3, Rad)

Sine 60° degrees
Sin(60, Deg)

Cosine of an angle Cos(x)

Notation:
Cos(x)
Cos(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cosine π/3 radians
Cos(π/3) or Cos(π/3, Rad)

Cosine 60° degrees
Cos(60, Deg)

Tangent of an angle Tan(x)

Notation:
Tan(x)
Tan(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Tangent π/3 radians
Tan(π/3) or Tan(π/3, Rad)

Tangent 60° degrees
Tan(60, Deg)

Cotangent of an angle Cot(x)

Notation:
Cot(x)
Cot(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cotangent π/3 radians
Cot(π/3) or Cot(π/3, Rad)

Cotangent 60° degrees
Cot(60, Deg)

Secant of an angle Sec(x)

Notation:
Sec(x)
Sec(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Secant π/3 radians
Sec(π/3) or Sec(π/3, Rad)

Secant 60° degrees
Sec(60, Deg)

Cosecant of an angle Csc(x)

Notation:
Csc(x)
Csc(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cosecant π/3 radians
Csc(π/3) or Csc(π/3, Rad)

Cosecant 60° degrees
Csc(60, Deg)

Inverse trigonometric functions
All inverse trigonometric functions take one or two arguments. If the function takes one argument, then the function will return the solution in radians.

Arcsine Asin(x)

Notation:
Asin(x)
Asin(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsine 1/3 (get the solution in radians)
Asin(1/3) or Asin(1/3, Rad)

Arcsine 1/3 (get the solution in degrees)
Asin(1/3, Deg)

Arccosine Acos(x)

Notation:
Acos(x)
Acos(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arccosine 1/3 (get the solution in radians)
Acos(1/3) or Acos(1/3, Rad)

Arccosine 1/3 (get the solution in degrees)
Acos(1/3, Deg)

Arctangent Atan(x)

Notation:
Atan(x)
Atan(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arctangent 1/3 (get the solution in radians)
Atan(1/3) or Atan(1/3, Rad)

Arctangent 1/3 (get the solution in degrees)
Atan(1/3, Deg)

Arccotangent Acot(x)

Notation:
Acot(x)
Acot(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arccotangent 1/3 (get the solution in radians)
Acot(1/3) or Acot(1/3, Rad)

Arccotangent 1/3 (get the solution in degrees)
Acot(1/3, Deg)

Arcsecant Asec(x)

Notation:
Asec(x)
Asec(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsecant 1/3 (get the solution in radians)
Asec(1/3) or Asec(1/3, Rad)

Arcsecant 1/3 (get the solution in degrees)
Asec(1/3, Deg)

Arcsecant Acsc(x)

Notation:
Acsc(x)
Acsc(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsecant 1/3 (get the solution in radians)
Acsc(1/3) or Acsc(1/3, Rad)

Arcsecant 1/3 (get the solution in degrees)
Acsc(1/3, Deg)

Expressions containing multiple embedding of functions and mathematical operations
Any expression can contain other expressions, the limit on the length of an expression is 100 characters.

Examples:
Root(Pow(3, 6), 2);
(5/2-4)*34/5-(Root(3, 2))
(12-123+5)/(12.45*(34/6))
Sin(60, Deg)+Cos(45, Deg)
etc.

Acceleration Calculator

Acceleration at uniformly accelerated (motion with constant acceleration), rectilinear motion is called a value equal to the ratio of the change in speed to the time interval during which this change occurred. The more the acceleration, the more the speed changes.

The SI unit of acceleration is meter per second squared, but other units can also be used, such as kilometer per hour squared, centimeter per second squared, etc.

Hours
Minutes
Seconds
Initial speed v0
Final speed v
The SI unit of acceleration

Final Speed Calculator

The final velocity v, which the object had at the end of the time interval t, is determined by the sum of the initial velocity v0 and the product of acceleration and time.

If v0 = 0, the formula takes the form v = at. So, if v0 is zero, put zero in the field for the initial speed v0.

The SI unit of speed is meter per second, but other units can also be used, such as kilometer per hour, centimeter per second, etc.

Hours
Minutes
Seconds
Initial speed v0
Acceleration a
The SI unit of final speed v

Initial Speed Calculator

The initial velocity v0 that the object had at time t0 is determined by the difference between the final speed v and the product of acceleration and time.

The SI unit of speed is meter per second, but other units can also be used, such as kilometer per hour, centimeter per second, etc.

Hours
Minutes
Seconds
Final speed v
Acceleration a
The SI unit of initial speed v0

Distance Calculator

Distance is defined as the sum of the product of the initial speed and time and the ratio of the product of acceleration and the square of time to 2.

With rectilinear uniformly accelerated motion without an initial speed, the distance is directly proportional to the square of the time interval during which this motion was made. Therefore, if the initial velocity v0 is zero, put zero in the field for the initial velocity v0, the equation becomes S = at²/2.

Hours
Minutes
Seconds
Speed v0
Acceleration a
The SI unit of distance S

Acceleration Calculation Examples

Example 1.
Before takeoff, the plane was moving uniformly accelerated for 45 seconds, determine the acceleration of the plane km/h² if in 45 seconds its speed increased from 15 to 100 m/s².
Step by step solution:

Convert meter per second to kilometer per hour.

Let's convert meters to kilometers. There are 1000 meters in one kilometer, so we divide the meters by 1000.
15 : 1000 = 3/200 = 0.015 kilometers.

Let's convert seconds to hours.
There are 3600 seconds in one hour, so we need to divide the number of seconds by 3600.
1 : 3600 = 1/3600

Divide distance by time

v₀ =	3/200
	1/3600

= 54 Kilometers per hour

Convert meter per second to kilometer per hour.

Let's convert meters to kilometers. There are 1000 meters in one kilometer, so we divide the meters by 1000.
100 : 1000 = 1/10 = 0.1 kilometers.

Let's convert seconds to hours.
There are 3600 seconds in one hour, so we need to divide the number of seconds by 3600.
1 : 3600 = 1/3600

Divide distance by time

v =	1/10
	1/3600

= 360 Kilometers per hour

Let's convert seconds to hours.
There are 3600 seconds in one hour, so we need to divide the number of seconds by 3600.
45 : 3600 = 1/80

Find the acceleration a, divide the difference between the initial and final speed by time.

Acceleration =

	360 - 54
	1/80

= 24480 Kilometers per hour squared

Example 2.
With what acceleration did the cyclist move if in 10 minutes his speed increased from 100 centimeters per second to 5.4 Kilometers per hour. Indicate the answer in km/s².
Step by step solution:

Convert centimeters per second to Kilometers per second.

Let's convert centimeters to kilometers. One kilometer has 100000 centimeters, so we divide centimeters by 100000.
100 : 100000 = 1/1000 = 0.001 kilometers.

We get
v₀ = 1/1000 = 0.001 Kilometers per second

Convert Kilometers per hour to Kilometers per second

Let's convert hours into seconds.
There are 3600 seconds in one hour, which means we need to multiply the number of hours by 3600.
1 × 3600 = 3600

Divide the resulting distance by time.

v =	5.4
	3600

= 3/2000 = 0.0015 Kilometers per second

Let's convert minutes to seconds.
One minute has 60 seconds, which means we need to multiply the number of minutes by 60.
10 × 60 = 600

Find the acceleration a, divide the difference between the initial and final speed by time.

Acceleration =

	3/2000 - 1/1000
	600

= 1/1200000 = 0.000000833333333333333 Kilometers per second squared

Examples of Calculating the Initial and Final Speed

Example 1.
What will be the speed of the object in 6 seconds if the object is moving with an acceleration of 3 m/s² and the initial speed is 5 m/s. Indicate the answer in inches per minute.
Step by step solution:

Convert meter per second to inch per minute

Let's convert meters to inches. There are 39.3701 inches in one meter, so multiply the meters by 39.3701.
5 × 39.3701 = 393701/2000 = 196.8505 inches.

Let's convert seconds to minutes.
One minute has 60 seconds, which means we need to divide the number of seconds by 60.
1 : 60 = 1/60

Divide distance by time

v₀ =	393701/2000
	1/60

= 1181103/100 = 11811.03 inches per minute

Convert meter per second square to inch per square minute

Let's convert meters to inches. There are 39.3701 inches in one meter, so multiply the meters by 39.3701.
3 × 39.3701 = 1181103/10000 = 118.1103 inches.

Let's convert seconds to minutes.
One minute has 60 seconds, which means we need to divide the number of seconds by 60.
1 : 60 = 1/60

Divide distance by time

a =	1181103/10000
	(1/60)²

= 10629927/25 = 425197.08 Inches per minute squared

Let's convert seconds to minutes.
One minute has 60 seconds, which means we need to divide the number of seconds by 60.
6 : 60 = 1/10

Let's find the final speed v, add to the initial speed v0 the product of acceleration a and time t.

Final speed v = 1181103/100 + (10629927/25) × 1/10 = 27165369/500 = 54330.738 Inches per minute

Example 2.
The object was moving with a constant acceleration of 4 centimeters per minute squared, after 1 hour the speed of the object was 10 Kilometers per hour, find the initial speed of the object. The answer is in meters per second.
Step by step solution:

Convert kilometer per hour to meter per second

Let's convert kilometers to meters. There are 1000 meters in one kilometer, so we multiply kilometers by 1000.
10 × 1000 = 10000 meters.

Let's convert hours into seconds.
There are 3600 seconds in one hour, which means we need to multiply the number of hours by 3600.
1 × 3600 = 3600

Divide distance by time

v =	10000
	3600

= 25/9 = 2.77777777777778 Meters per second

Convert centimeter by minute squared to meter per second squared

Let's convert centimeters to meters. One meter has 100 centimeters, so we divide centimeters by 100.
4 : 100 = 1/25 = 0.04 meters.

Let's convert minutes to seconds.
One minute has 60 seconds, which means we need to multiply the number of minutes by 60.
1 × 60 = 60

Divide distance by time

a =	1/25
	60²

= 1/90000 = 0.0000111111111111111 Meter per second squared

Let's convert hours into seconds.
There are 3600 seconds in one hour, which means we need to multiply the number of hours by 3600.
1 × 3600 = 3600

Let us find the initial speed v0, subtract the product of acceleration a by time t from the final speed v.

Initial speed v0 = 25/9 - (1/90000) × 3600 = 616/225 = 2.73777777777778 Meters per second

Examples of Calculating the Distance Traveled With Rectilinear Uniformly Accelerated Motion

Example 1.
The cyclist left the mountain in 1 minute 10 seconds, moving with a constant acceleration of 0.7 m/s² Calculate the length of the slide if it is known that at the beginning of the descent the speed of the cyclist was 21 km/h. Express the answer in centimeters.
Step by step solution:

Convert kilometer per hour to meter per second

Let's convert kilometers to meters. There are 1000 meters in one kilometer, so we multiply kilometers by 1000.
21 × 1000 = 21000 meters.

Let's convert hours into seconds.
There are 3600 seconds in one hour, which means we need to multiply the number of hours by 3600.
1 × 3600 = 3600

Divide distance by time

v₀ =	21000
	3600

= 35/6 = 5.83333333333333 Meters per second

Let's convert minutes to seconds.
One minute has 60 seconds, which means we need to multiply the number of minutes by 60.
1 × 60 = 60

Add up the resulting number of seconds
60 + 10 = 70 seconds.

Let us find the length, calculate the sum of the product of the initial speed and time and the ratio of the product of acceleration and the square of time to 2.

Length L = 35/6 × 70 +

	0.7 × 70²
	2

= 6370/3 = 2123.33333333333 meters.

Let's convert meters to centimeters. There are 100 centimeters in one meter, so we multiply the meters by 100.
6370/3 × 100 = 637000/3 = 212333.333333333 centimeters.

Length L = 637000/3 = 212333.333333333 centimeters.

See also