Magnitude of Acceleration Calculator

This magnitude of acceleration calculator in physics helps determine the magnitude of an acceleration vector, which is essential for analyzing the motion of objects.

Two masses, m1 = 5 kg and m2 = 10 kg, and they are connected in such a way that m1 pulls m2 with a force of F = 50 N:

Calculate the acceleration of m2:

a = F/m2 = 50 N/10 kg = 5 m/s^2 This means that m2 will accelerate at 5 m/s^2 due to the force exerted by m1.

Magnitude of Acceleration Calculator

ax (m/s²)	ay (m/s²)	az (m/s²)	Magnitude of Acceleration (m/s²)
3	4	0	5
-2	5	6	8.06
10	0	0	10
1	1	1	1.73
-5	12	-4	13.75
0	0	0	0
5	-3	2	6.16
15	15	0	21.21
20	0	0	20
30	0	0	30
0	9.81	0	9.81
0	0	30	30
1.33 x 10¹⁴	0	0	1.33 x 10¹⁴
49	0	0	49
88	0	0	88
333	0	0	333
454	0	0	454[2].

Magnitude of Acceleration Formula

The formula for calculating the magnitude of acceleration is:

|a| = √(ax² + ay² + az²)

Where:

• |a| is the magnitude of acceleration
• ax, ay, and az are the acceleration components in the x, y, and z directions, respectively

In cases where motion is confined to a single plane or line, the formula simplifies to:

|a| = √(ax² + ay²) or |a| = |ax|

Consider a rocket launching vertically. If it experiences an upward acceleration of 30 m/s², the magnitude of acceleration would simply be 30 m/s².

How do you calculate the magnitude of acceleration?

1. Identify the acceleration components: Determine the acceleration in each relevant direction (x, y, and z if applicable).
2. Square each component: Calculate the square of each acceleration component.
3. Sum the squared values: Add all the squared components together.
4. Take the square root: The square root of the sum gives you the magnitude of acceleration.

A drone is moving with accelerations of 3 m/s² eastward (x-direction), 4 m/s² northward (y-direction), and 2 m/s² upward (z-direction).

Identify components: ax = 3 m/s², ay = 4 m/s², az = 2 m/s²

Square components: ax² = 9, ay² = 16, az² = 4

Sum squared values: 9 + 16 + 4 = 29

Take square root: √29 ≈ 5.39 m/s²

The magnitude of acceleration for the drone is approximately 5.39 m/s².

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