The shark can accelerate to a speed of 32.0 km/h in a few seconds. Assume that it takes a shark 1.5 s to accelerate uniformly from 2.8 km/h to 32.0 km/h. What is the magnitude of the shark's acceleration?
To find the magnitude of the shark's acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 2.8 km/h
Final velocity (v) = 32.0 km/h
Time (t) = 1.5 seconds
First, we need to convert the given velocities from km/h to m/s, as the SI unit for acceleration is in m/s^2:
initial velocity (u) = 2.8 km/h = (2.8 * 1000) / 3600 m/s = 0.7778 m/s
final velocity (v) = 32.0 km/h = (32.0 * 1000) / 3600 m/s = 8.8889 m/s
Now, we can substitute the values into the formula:
acceleration = (8.8889 m/s - 0.7778 m/s) / 1.5 seconds
acceleration = 8.1111 m/s / 1.5 seconds
Therefore, the magnitude of the shark's acceleration is approximately 5.4074 m/s^2.
To find the magnitude of the shark's acceleration, we can use the relation:
acceleration = (final velocity - initial velocity) / time
Given:
- Initial velocity (u) = 2.8 km/h = 2.8 * (1000/3600) m/s = 0.7778 m/s
- Final velocity (v) = 32.0 km/h = 32.0 * (1000/3600) m/s = 8.8889 m/s
- Time (t) = 1.5 s
Using the formula:
acceleration = (v - u) / t
Substituting the given values:
acceleration = (8.8889 - 0.7778) / 1.5
Simplifying:
acceleration = 8.1111 / 1.5
acceleration ≈ 5.4074 m/s²
Therefore, the magnitude of the shark's acceleration is approximately 5.4074 m/s².