Question

The highest speed attained by a cyclist on level ground is 105 km/h. To attain this speed, the cyclist used a streamlined recumbent bike. Starting from rest, he gradually built up his speed by pedaling furiously over a distance of 3.2 km. If his acceleration was uniform over this distance, what was the acceleration and how long did the cyclist take to build up his final speed

Answer 1

The acceleration is 0.133 m/s²

The time taken to build the final speed is 219.32 s

Step-by-step explanation:

Given;

final speed of the cyclist, v = 105 km/h = 29.17 m/s²

distance traveled by the cyclist, d = 3.2 km = 3,200 m

initial speed, u = 0

Apply the following kinematic equation to determine the acceleration of the cyclist;

v² = u² + 2as

(29.17 )² = 0 + (2 x 3200)a

850.89 = 6400a

a = (850.89 ) / (6400)

a = 0.133 m/s²

The time taken to build up the final speed is given by;

v = u + at

29.17 = 0 + (0.133)t

t = 29.17 / 0.133

t = 219.32 s