As she climbs a hill, a cyclist slows down from 25 mph to 6 mph and 10 seconds what is her deceleration?
To calculate the deceleration, we can use the formula:
Acceleration (deceleration) = (final velocity - initial velocity) / time
Given:
Initial velocity (vi) = 25 mph
Final velocity (vf) = 6 mph
Time (t) = 10 seconds
Deceleration = (6 mph - 25 mph) / 10 s
Before proceeding with the calculation, we need to ensure that both velocities are in the same units. Let's convert the velocities from mph to m/s:
1 mph = 0.44704 m/s
Initial velocity in m/s:
vi = 25 mph * 0.44704 m/s = 11.176 m/s
Final velocity in m/s:
vf = 6 mph * 0.44704 m/s = 2.68224 m/s
Now, we can substitute the values into the formula:
Deceleration = (2.68224 m/s - 11.176 m/s) / 10 s
Calculating:
Deceleration = -8.49376 m/s / 10 s
Deceleration ≈ -0.8494 m/s²
Therefore, the cyclist's deceleration while climbing the hill is approximately -0.8494 m/s². The negative sign indicates deceleration since the cyclist is slowing down.