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?
- Identify the acceleration components: Determine the acceleration in each relevant direction (x, y, and z if applicable).
- Square each component: Calculate the square of each acceleration component.
- Sum the squared values: Add all the squared components together.
- 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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