At the starting gun a runner accelerates from the rest at 1.5 m/s squared for 2.2 seconds. What is the runner's speed 2.0 seconds after she starts running?
Well, I hope the runner doesn't get too tired running away from her problems! Let's calculate her speed, shall we?
During the first 2.2 seconds, the runner accelerates at a rate of 1.5 m/s². So, after 2.2 seconds, her speed is given by the equation:
v = u + at
Where:
v = final velocity
u = initial velocity (0 m/s, since she starts from rest)
a = acceleration (1.5 m/s²)
t = time (2.2 seconds)
Plugging the values into the equation:
v = 0 + (1.5 m/s²) * (2.2 s)
v = 0 + 3.3 m/s
Therefore, the runner's speed 2.0 seconds after she starts running is 3.3 m/s. Looks like she's picking up the pace!
To find the runner's speed 2.0 seconds after she starts running, we can break the problem into two parts: the initial acceleration phase and the constant speed phase.
During the initial acceleration phase, we use the equation:
v = u + at
where:
v = final velocity
u = initial velocity (0 m/s in this case as the runner starts from rest)
a = acceleration (1.5 m/s^2)
t = time (2.2 seconds)
Plugging in the values, we can calculate the velocity at the end of the acceleration phase:
v = 0 + (1.5 m/s^2) * (2.2 s)
v = 3.3 m/s
So, after 2.2 seconds, the runner's speed is 3.3 m/s.
Next, we need to find the runner's speed after an additional 2.0 seconds. Since the runner is no longer accelerating, her speed remains constant after the initial acceleration phase.
To calculate the speed during the constant speed phase, we can use the equation:
v = u + at
where:
v = final velocity (which is the same as the initial velocity after the acceleration phase)
u = initial velocity (3.3 m/s in this case)
a = acceleration (0 m/s^2 as there is no further acceleration)
t = time (2.0 seconds)
Plugging in the values, we can determine the velocity after the additional 2.0 seconds:
v = 3.3 m/s + (0 m/s^2) * (2.0 s)
v = 3.3 m/s
Therefore, after a total of 4.2 seconds, the runner's speed is still 3.3 m/s.