Pablo is running down the street at 10.0 meters per second. He sees a $20 bill on the road ahead of him and
starts sprinting. After 5.0 seconds have passed, Pablo is running at 15.0 meters per second. Assuming he does
not change direction, what was Pablo’s acceleration?
Acceleration is the rate of change of velocity over time. To find Pablo's acceleration, we need to calculate the change in velocity and divide it by the change in time.
The change in velocity is calculated by subtracting the initial velocity from the final velocity:
Change in velocity = Final velocity - Initial velocity
Given that Pablo's initial velocity is 10.0 m/s and his final velocity is 15.0 m/s, we can plug these values into the equation:
Change in velocity = 15.0 m/s - 10.0 m/s
Subtracting these values, we get:
Change in velocity = 5.0 m/s
Now, we need to calculate the change in time. The problem states that 5.0 seconds have passed, which means the change in time is 5.0 seconds.
Finally, we can calculate the acceleration by dividing the change in velocity by the change in time:
Acceleration = Change in velocity / Change in time
Plugging in the values, we get:
Acceleration = 5.0 m/s / 5.0 s
Simplifying this, we find that Pablo's acceleration is:
Acceleration = 1.0 m/s²
To find Pablo's acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 10.0 m/s
Final velocity (v) = 15.0 m/s
Time (t) = 5.0 s
Using the formula, we can calculate the acceleration by substituting the values:
acceleration = (15.0 - 10.0) / 5.0
Simplifying the equation:
acceleration = 5.0 / 5.0
Therefore, Pablo's acceleration is 1.0 m/s².