Question

Shanda Lear decelerates her motorcycle at a rate of 0.83 m/s² in order to avoid debris in the road. If it takes her 4.1 seconds to slow down to 7.9 m/s, what was the initial velocity she was riding at?

A) 12.27 m/s
B) 13.02 m/s
C) 8.91 m/s
D) 15.39 m/s

Answer 1

Shanda Lear's initial velocity was approximately 11.3 m/s before she began to decelerate. This value is calculated using the kinematic equation for uniformly accelerated motion, but it does not match any of the provided options.

Step-by-step explanation:

To determine Shanda Lear's initial velocity before she began to decelerate, we will use the kinematic equation for uniformly accelerated motion:

v = u + at

Where:
v is the final velocity (7.9 m/s),
u is the initial velocity (which we are trying to find),
a is the acceleration (-0.83 m/s², negative because it is deceleration),
t is the time (4.1 seconds).

Rearranging the equation to solve for the initial velocity gives:

u = v - at

Plugging in the values gives:

u = 7.9 m/s - (-0.83 m/s² × 4.1 s)

u = 7.9 m/s + 3.403 m/s

u = 11.303 m/s

Therefore, the initial velocity Shanda Lear was riding at was 11.303 m/s, which is not one of the answer choices provided. Her actual initial velocity would be approximately 11.3 m/s, suggesting either a calculation or typographical error in the question options.