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?
acceleration = changevelocity/time
changevelocity= 29.2km/hr*1hr/3600sec*10^3m/km=8.11m/s
Well, it seems like the shark is quite the speedster! Let's calculate its acceleration, shall we?
To find the magnitude of the shark's acceleration, we need to use the formula:
acceleration = (final velocity - initial velocity) / time
So let's plug in the values we have:
acceleration = (32.0 km/h - 2.8 km/h) / 1.5 s
Now, let's do some unit conversion. We'll convert km/h to m/s since it's the standard unit for acceleration.
1 km/h = 1000 m / 3600 s
So let's convert the velocities:
final velocity = 32.0 km/h * (1000 m / 3600 s) = 8.89 m/s
initial velocity = 2.8 km/h * (1000 m / 3600 s) = 0.78 m/s
Now we can calculate the acceleration:
acceleration = (8.89 m/s - 0.78 m/s) / 1.5 s
And the answer is... drumroll, please...
The magnitude of the shark's acceleration is approximately 5.07 m/s².
That's a pretty impressive swimming speed for a fish with killer instincts!
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
Let's convert the velocities from km/h to m/s to ensure consistent units:
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
Substituting 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
acceleration = 5.4074 m/s² (rounded to four decimal places)
Therefore, the magnitude of the shark's acceleration is approximately 5.4074 m/s².
To find the magnitude of the shark's acceleration, we can use the formula:
acceleration = (change in velocity) / (time)
Here, the change in velocity is the final velocity minus the initial velocity.
Given:
Initial velocity (u) = 2.8 km/h
Final velocity (v) = 32.0 km/h
Time (t) = 1.5 s
First, let's convert the velocities from km/h to m/s, as the SI unit of acceleration is m/s^2.
Initial velocity (u) = 2.8 km/h × (1000 m/1 km) × (1 h/3600 s) = 0.78 m/s
Final velocity (v) = 32.0 km/h × (1000 m/1 km) × (1 h/3600 s) = 8.89 m/s
Now, we can calculate the change in velocity:
(change in velocity) = final velocity - initial velocity
(change in velocity) = 8.89 m/s - 0.78 m/s = 8.11 m/s
Finally, we can plug the values into the formula to calculate the magnitude of acceleration:
acceleration = (change in velocity) / (time)
acceleration = 8.11 m/s / 1.5 s = 5.407 m/s^2
Therefore, the magnitude of the shark's acceleration is approximately 5.407 m/s^2.