A car enters the freeway with a speed of 6.5
m/s and accelerates uniformly for 3.5 km in
3.9 min.
How fast is the car moving after this time?
Answer in units of m/s.
3500 = 0 + 6.5 t + (1/2)a t^2
but t = 3.9*60 = 234 seconds
3500 = 6.5 * 234 + (1/2) a (234^2)
3500 = 1521 + 27378 a
a = .0723 m/s^2
v = Vi + a t
v = 6.5 + .0723 * 234
= 6.5+16.9 = 23.4 m/s
A car enters the freeway with a speed of 5.6 m/s and accelerates uniformly for 2.7 km in 3.0 min. How fast is the car moving after this time? Answer in units of m/s
212
To find the final speed of the car, we can use the equation of motion that relates the final speed (vf), initial speed (vi), acceleration (a), and time (t):
vf = vi + at
In this case, the initial speed (vi) is 6.5 m/s, the time (t) is 3.9 minutes (which we need to convert to seconds), and we need to find the final speed (vf). We also need to find the acceleration (a) using the given information.
The car accelerates uniformly for 3.5 km, so we can convert this distance to meters by multiplying it by 1000.
Let's calculate the acceleration (a) first:
Acceleration (a) = Change in speed (Δv) / Time (t)
The change in speed (Δv) is the difference between the final speed (vf) and the initial speed (vi).
Δv = vf - vi
We know the initial speed (vi) is 6.5 m/s, but we don't know the final speed (vf) yet. However, we can use another equation of motion that relates distance (d), initial speed (vi), final speed (vf), acceleration (a), and time (t):
d = vit + 0.5at^2
Rearranging this equation, we can solve for the acceleration (a):
a = (2d - 2vi*t) / t^2
Substituting the given values, we have:
a = (2 * 3.5 km * 1000 - 2 * 6.5 m/s * 3.9 min * 60 s/min) / (3.9 min * 60 s/min)^2
Now we can calculate the acceleration (a) using a calculator.
After calculating the acceleration (a), we can substitute it into the first equation to find the final speed (vf):
vf = vi + at
Substituting the values we know:
vf = 6.5 m/s + a * 3.9 min * 60 s/min
Simplify and calculate the final speed (vf) using a calculator.
The final speed of the car is the result in units of m/s.