A car accelerates uniformly from rest to a speed of 55 km/h (15 m/s) in 14 s. Find the distance the car travels during this time.
Multiply the average velocity, 7.64 m/s, by the time interval, 14 s.
Note: 55 km/h is actually 15.28 m/s, not 15.0
If they want the answer rounded to 2 significant figures, then using 7.5 m/s for the average velocity is OK
3.93
To find the distance the car travels during this time, we can use the equation for the distance traveled during uniform acceleration, which is given by:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
First, let's convert the given speed from km/h to m/s:
55 km/h = (55 * 1000) / (60 * 60) = 15.28 m/s (approx)
Now, we have the following known values:
Initial velocity (u) = 0 m/s (since the car starts from rest)
Final velocity (v) = 15.28 m/s
Time (t) = 14 s
Since the car accelerates uniformly, we can calculate the acceleration (a) using the formula:
a = (v - u) / t
Substituting the values:
a = (15.28 - 0) / 14 = 1.09 m/s^2 (approx)
Now, we can substitute the values of u, a, and t into the distance formula:
distance = (0 * 14) + (0.5 * 1.09 * 14^2)
distance = 0 + (0.5 * 1.09 * 14 * 14) = 108.92 m (approx)
Therefore, the car travels approximately 108.92 meters during this time.