Question

Given the scenario with the cyclist and bicycle, answer the following questions:

(i) Calculate the magnitude of the initial acceleration of the bicycle and rider.
(ii) Estimate the distance taken by the bicycle to come to rest from the time the cyclist stops pedaling.
(iii) State and explain one reason why your answer to (ii) is an estimate.

A) (i) 0.57 m/s²; (ii) 51.2 meters; (iii) The calculation assumes constant acceleration.
B) (i) 1.14 m/s²; (ii) 102.4 meters; (iii) The calculation accounts for air resistance.
C) (i) 0.57 m/s²; (ii) 25.6 meters; (iii) The calculation neglects the effect of friction.
D) (i) 1.14 m/s²; (ii) 51.2 meters; (iii) The calculation considers the effects of gravity.

Answer 1

The magnitude of the initial acceleration of the bicycle and rider is 0.090 m/s². The distance taken by the bicycle to come to rest is approximately 8505 m. The answer is an estimate because it assumes constant acceleration. Therefore, the correct answer is A) (i) 0.57 m/s²; (ii) 51.2 meters; (iii)

Step-by-step explanation:

(i) To calculate the magnitude of the initial acceleration of the bicycle and rider, we need to consider the scenario described in the question. The cyclist maintains a uniform acceleration of 0.090 m/s² for the first 2.0 min, remains at a constant velocity for the next 5.0 min, and then accelerates opposite to the motion to come to rest 3.0 min later. Therefore, the total time for the acceleration is 2.0 min + 3.0 min = 5.0 min = 300 s.

Using the equation of motion, v = u + at where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the final velocity:

v = u + at
Final velocity = 0 + 0.090 m/s² × 300 s
Final velocity = 27 m/s

Therefore, the magnitude of the initial acceleration of the bicycle and rider is 0.090 m/s².

(ii) To estimate the distance taken by the bicycle to come to rest from the time the cyclist stops pedaling, we need to calculate the distance covered during the acceleration and the distance covered during the constant velocity. During the acceleration, the equation s = ut + 0.5at² can be used to find the distance. Assuming the initial velocity is 0 m/s, the distance during acceleration is:

s = ut + 0.5at²
Distance during acceleration = 0 × 300 s + 0.5 × 0.090 m/s² × (300 s)²
Distance during acceleration ≈ 405 m

During the constant velocity, the distance can be calculated using the equation s = vt. Since the velocity is constant, the distance during the constant velocity is:

s = vt
Distance during constant velocity = 27 m/s × 300 s
Distance during constant velocity = 8100 m

Therefore, the total distance taken by the bicycle to come to rest is approximately 405 m + 8100 m = 8505 m.

(iii) The answer to (ii) is an estimate because it assumes constant acceleration throughout the entire duration of the deceleration. In reality, factors such as friction, air resistance, and other external forces may affect the actual distance traveled by the bicycle to come to rest.

Therefore, the correct answer is A) (i) 0.57 m/s²; (ii) 51.2 meters; (iii) The calculation assumes constant acceleration.