Sara walks at 1.50 m/s. She notices Emily is standing at the coffee shop ahead so she accelerates at 1.55 m/s ^2. How far is emily ?
To find the distance Emily is from Sara, we can use the equations of motion.
First, let's find the time it takes for Sara to accelerate from her initial velocity to her final velocity.
The equation for finding the time with constant acceleration is:
vf = vi + at
where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
In this case, Sara's initial velocity (vi) is 1.50 m/s, her final velocity (vf) will be the velocity she reaches after accelerating, and her acceleration (a) is 1.55 m/s^2.
Since she is initially stationary and accelerates, her final velocity will be:
vf = vi + at
vf = 1.50 m/s + (1.55 m/s^2) * t
Now, we can find the time (t) it takes for her to reach that velocity.
To do so, we use another equation of motion:
t = (vf - vi) / a
Substituting the values:
t = (vf - vi) / a
t = (vf - 1.50 m/s) / (1.55 m/s^2)
Next, we need to find the distance (d) that Sara would have traveled during this time.
The equation for finding distance with constant acceleration is:
d = vit + 0.5at^2
where:
d = distance
vi = initial velocity
a = acceleration
t = time
Since Sara starts from rest, her initial velocity is 0 m/s.
Plugging in the values:
d = (0 m/s)(t) + 0.5(1.55 m/s^2)(t^2)
d = 0.775 m/s^2(t^2)
So, the distance Sara would have traveled during this time is 0.775 m/s^2 multiplied by the square of the time it took her to reach the final velocity.
Now, you can substitute the value of t back in, and solve for d to get the distance Emily is from Sara.