Answer:
Explanation:
To find the cyclist’s acceleration, we can use the formula for acceleration, which is a = (v_f - v_i) / t, where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time it takes to accelerate from v_i to v_f. However, we do not have the value of t in this problem. Instead, we can use another formula that relates distance, initial velocity, final velocity, and acceleration: d = (v_i + v_f) * t / 2, where d is the distance traveled.
First, let’s convert the given velocities from km/h to m/s. 10 km/h is equivalent to (10 * 1000) / (60 * 60) = 2.7778 m/s, and 26 km/h is equivalent to (26 * 1000) / (60 * 60) = 7.2222 m/s. Now we can substitute the given values into the formula for distance: 1.6 * 1000 = (2.7778 + 7.2222) * t / 2. Solving for t, we get t = (1.6 * 1000 * 2) / (2.7778 + 7.2222) ≈ 320 s.
Now that we have the value of t, we can use the formula for acceleration to find the cyclist’s acceleration: a = (7.2222 - 2.7778) / 320 ≈ 0.0139 m/s^2. So, the cyclist’s acceleration is approximately 0.0139 m/s^2.