A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 2.9 km in3.4 min.
How fast is the car moving after this time?
Answer in units of m/s
To find the final speed of the car after the given time, we need to convert the given values to consistent units and use the kinematic equation of motion.
First, let's convert the distance from kilometers to meters. Since 1 kilometer equals 1000 meters, 2.9 km is equal to 2.9 * 1000 = 2900 meters.
Next, let's convert the time from minutes to seconds. Since 1 minute equals 60 seconds, 3.4 minutes is equal to 3.4 * 60 = 204 seconds.
Now we have the following information:
Initial speed (u) = 6.4 m/s
Distance (s) = 2900 meters
Time (t) = 204 seconds
Using the equation of motion: s = ut + (1/2)at^2, where 'a' is the acceleration, we can solve for 'a'.
Since the car is accelerating uniformly, we can assume its acceleration (a) is constant throughout the motion. Also, the initial speed (u) in this equation is 0 since the car starts from rest in the beginning.
Rearranging the equation, we have: 2as = s = ut^2
Simplifying, we get: a = 2s / t^2
a = 2 * 2900 / (204)^2
a ≈ 0.0024 m/s^2
Next, we can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Substituting the values, we get: v = 6.4 + 0.0024 * 204
v ≈ 6.8848 m/s
Therefore, the car is moving at approximately 6.8848 m/s after the given time.