a motorized scooter starts from rest and accelerates for 4 s at 2 m/s2. it continues at a constant speed for 6 s . What is the scooter's average velocity for the interval 0-4 s ?
the scooters average velocity is 2 m/s
To find the average velocity for the interval 0-4 seconds, we need to determine the scooter's final velocity at the end of the 4-second acceleration period.
Using the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity (which is 0 since the scooter starts from rest), a is the acceleration (2 m/s^2), and t is the time interval (4 seconds), we can calculate the final velocity:
v = 0 + (2 m/s^2)(4 s)
v = 8 m/s
Since the scooter continues at a constant speed for the next 6 seconds, the average velocity for this interval is equal to the final velocity, which is 8 m/s.
To find the scooter's average velocity for the interval 0-4 s, we need to determine its displacement during that time period. The average velocity is defined as the total displacement divided by the total time.
In this problem, the scooter starts from rest and accelerates for 4 seconds at a constant acceleration of 2 m/s^2. We can use the kinematic equation for displacement to find how far the scooter has traveled during the first 4 seconds.
The equation for displacement is given by:
d = vit + (1/2)at^2
where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.
Since the scooter starts from rest (vi = 0), the equation simplifies to:
d = (1/2)at^2
Plugging in the values for acceleration (a = 2 m/s^2) and time (t = 4 s), we have:
d = (1/2)(2)(4)^2 = 16 m
Therefore, the scooter's displacement during the first 4 seconds is 16 m.
Now, we can calculate the average velocity using the formula:
Average velocity = total displacement / total time
In this case, the total displacement is 16 m and the total time is 4 s. So, the average velocity is:
Average velocity = 16 m / 4 s = 4 m/s
Hence, the scooter's average velocity for the interval 0-4 s is 4 m/s.