Answer:
d = 1500 m
v = 16.7 m/s
Explanation:
Since the cyclist moves with constant acceleration, we can use kinematic equations, also known as SUVAT equations, to find the cyclist's speed at the end of his acceleration. We can then find the distance the cyclist travels by finding the area underneath the velocity-time graph. Finally, we can calculate the average velocity as equal to the total distance divided by the total time.
The kinematic equation we will use is:
v = u + at
where
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is time
Given that the cyclist starts from rest and accelerates at 1 m/s² for 20 s, the final speed of the cyclist is:
v = (0 m/s) + (1 m/s²) (20 s)
v = 20 m/s
The cyclist maintains this speed for an additional minute (60 seconds). Then the cyclist decelerates to a stop after 10 seconds. The velocity time graph will be as shown.
The total distance traveled is equal to the area under the graph. We can divide the region into a triangle, a rectangle, and another triangle.
d = ½ (20 s) (20 m/s) + (60 s) (20 m/s) + ½ (10 s) (20 m/s)
d = 200 m + 1200 m + 100 m
d = 1500 m
The average velocity is the total distance over the total time.
v = 1500 m / (20 s + 60 s + 10 s)
v = 16.7 m/s
