A bicyclist starts from rest and accelerates at 4 m/s^2 for 3 seconds. The cyclist then travels for 20s at a constant speed. How far does the cyclist travel?
I got 138 m but I'm not sure if I'm right?
you're not
accelerates to 12 m/s, then travels for 20 s
... that's 240 m, plus the acceleration distance
d = 1/2 a t^2
To calculate the distance traveled by the cyclist, we need to break down the problem into two parts: acceleration and constant speed.
First, let's calculate the distance covered during the acceleration phase. We can use the equation:
distance = initial velocity * time + 1/2 * acceleration * time^2
Given that the initial velocity is zero (since the cyclist starts from rest), and the acceleration is 4 m/s^2, and the time is 3 seconds, we can substitute these values into the equation to find the distance traveled during the acceleration phase:
distance_acceleration = 0 * 3 + 1/2 * 4 * (3^2)
= 0 + 1/2 * 4 * 9
= 0 + 1/2 * 36
= 0 + 18
= 18 meters
Therefore, the cyclist travels 18 meters during the acceleration phase.
Next, let's calculate the distance covered during the constant speed phase. Since the speed is constant, we can simply multiply the speed (which is the same as the final velocity) by the time. Given that the time is 20 seconds, and the speed is constant, we can use the equation:
distance_constant_speed = speed * time
We haven't been given the speed, but we know that it's constant, which means it remains the same once the acceleration phase ends. Therefore, the speed at the end of the acceleration phase is equal to the speed during the constant speed phase.
To find the speed at the end of the acceleration phase, we can use the equation:
final velocity = initial velocity + acceleration * time
Given that the initial velocity is zero (since the cyclist starts from rest), the acceleration is 4 m/s^2, and the time is 3 seconds, we can substitute these values into the equation to find the speed at the end of the acceleration phase:
final velocity = 0 + 4 * 3
= 0 + 12
= 12 m/s
Therefore, the cyclist travels at a constant speed of 12 m/s during the 20-second period.
Now, we can calculate the distance covered during the constant speed phase:
distance_constant_speed = speed * time
= 12 * 20
= 240 meters
Therefore, the cyclist travels 240 meters during the constant speed phase.
To find the total distance traveled, we add the distance covered during the acceleration phase to the distance covered during the constant speed phase:
total distance = distance_acceleration + distance_constant_speed
= 18 + 240
= 258 meters
Hence, the cyclist travels a total distance of 258 meters.