a car eneters a freeway with a speed of 6.7 m\s and accelerates uniformly for 3.0 I 3.8 min . how fas the car moving after this time?
To find the final speed of the car after accelerating uniformly, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 6.7 m/s
t = 3.0 min = 3.0 * 60 = 180 seconds
Now, we need to find the acceleration first. Acceleration can be calculated using the equation:
a = (v - u) / t
Rearranging the equation, we get:
v = u + at
Substituting the known values:
a = (v - 6.7) / 180
Since the car is accelerating uniformly, we can assume a constant acceleration. Therefore, we can use the average acceleration for the given time period.
Now, we need to convert the time from minutes to seconds. Given t = 3.8 min, we have:
t = 3.8 * 60 = 228 seconds
Substituting the values into the equation, we get:
a = (v - 6.7) / 228
Now, equating the expressions for acceleration:
(v - 6.7) / 180 = (v - 6.7) / 228
Cross-multiplying, we have:
228(v - 6.7) = 180(v - 6.7)
228v - 1527.6 = 180v - 1206
Collecting like terms:
228v - 180v = 1527.6 - 1206
48v = 321.6
Dividing both sides by 48:
v = 6.7 + (321.6 / 48)
v = 6.7 + 6.7
v = 13.4 m/s
Therefore, the car is moving at a speed of 13.4 m/s after 3.8 minutes of uniform acceleration.