Riding his bike, Dewayne can start from rest and get going at 12 m/s in 4 seconds. Beth can get going 16 m/s in 5 seconds. Who has a greater acceleration? How do you know?
Beth has a faster acceleration because you divide speed by time, and Beth is 16/5= 3.2, whereas Dewayne is 12/4= 3.
To determine who has a greater acceleration, we need to calculate the acceleration for both Dewayne and Beth. Acceleration is defined as the change in velocity divided by the time it takes to change. The formula for acceleration is:
Acceleration (a) = (final velocity - initial velocity) / time
Let's calculate the acceleration for Dewayne and Beth.
For Dewayne:
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 12 m/s
Time (t) = 4 seconds
Acceleration (Dewayne) = (12 m/s - 0 m/s) / 4 seconds = 12 m/s / 4 seconds = 3 m/s²
For Beth:
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 16 m/s
Time (t) = 5 seconds
Acceleration (Beth) = (16 m/s - 0 m/s) / 5 seconds = 16 m/s / 5 seconds = 3.2 m/s²
Now, comparing the accelerations:
Dewayne's acceleration = 3 m/s²
Beth's acceleration = 3.2 m/s²
Since Beth's acceleration (3.2 m/s²) is greater than Dewayne's acceleration (3 m/s²), Beth has a greater acceleration.
Thus, Beth has a greater acceleration than Dewayne, as calculated.