Final answer:
Sandra's acceleration while slowing down on her bicycle is -0.8 meters/second², calculated using the change in velocity over time.
Step-by-step explanation:
Sandra is riding a bicycle and experiences a change in velocity from 10.0 meters/second to 2.0 meters/second in 10 seconds. To find her acceleration, we use the formula ℇ = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time taken. Plugging in the values, we get ℇ = (2.0 m/s - 10.0 m/s) / 10 s = -0.8 m/s². This means her acceleration is -0.8 meters/second² (option a.), indicating she is slowing down.
Acceleration is the rate of change of velocity over time. In Sandra's case, her initial velocity is 10.0 meters/second, and she slows down to 2.0 meters/second in a time span of 10 seconds. The formula for acceleration (a) is given by the change in velocity (Δv) divided by the time (Δt):
�
=
Δ
�
Δ
�
a=
Δt
Δv
Substitute the given values:
�
=
(
2.0
m/s
−
10.0
m/s
)
10
s
a=
10s
(2.0m/s−10.0m/s)
�
=
−
8.0
m/s
10
s
a=
10s
−8.0m/s
�
=
−
0.8
m/s²
a=−0.8m/s²
The negative sign indicates that Sandra is decelerating or slowing down. Therefore, Sandra's acceleration is
−
0.8
m/s²
−0.8m/s². This means that her velocity decreases by 0.8 meters per second every second.