Final answer:
To calculate the time for Mr. Cheung to reach the bus stop, we consider the acceleration period and the constant speed travel. Mr. Cheung's total time to reach the bus stop is 8.9 seconds after accelerating for 2 seconds and running at his new constant speed.
Step-by-step explanation:
To calculate the time needed for Mr. Cheung to reach the bus stop, we'll break down his journey into two parts: his initial walk at 1.6 m/s and his acceleration followed by running at the new speed.
First, Mr. Cheung speeds up at an acceleration of 1.2 m/s² for 2 seconds. The increase in speed (Δv) can be found using the formula Δv = a × t, where 'a' is acceleration and 't' is time. Hence the increase in speed is 1.2 m/s² × 2 s = 2.4 m/s. His new speed becomes 1.6 m/s + 2.4 m/s = 4.0 m/s.
Mr. Cheung covers some distance during the acceleration. Using the formula d = ½ a t², where 'd' is the distance, we find that distance to be ½ × 1.2 m/s² × (2 s)² = 2.4 m. So, he has 30 m - 2.4 m = 27.6 m left to travel at his new constant speed of 4.0 m/s. The time taken to cover this distance at constant speed is t = d / v = 27.6 m / 4.0 m/s = 6.9 seconds.
Adding the 2 seconds of acceleration to the 6.9 seconds of running, we find that the total time for Mr. Cheung to reach the bus stop is 2 s + 6.9 s = 8.9 seconds.