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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.


Acceleration Calculator

Acceleration  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

Final speed vThe 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

Initial speed v0The 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

DistanceDistance 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 ร— 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 ร— 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 ร— 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 ร— 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) ร— 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 ร— 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 ร— 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 ร— 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 ร— 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) ร— 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 ร— 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 ร— 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 ร— 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 ร— 70 +
0.7 ร— 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 ร— 100 = 637000/3 = 212333.333333333 centimeters.

Length L = 637000/3 = 212333.333333333 centimeters.




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