A car starts from rest and accelerates uniformly for 10 seconds. During this time, it covers a distance of 200 meters. Find the displacement of the car during this interval.
We know that the car starts from rest, so its initial velocity (u) is 0 m/s. The time taken (t) is 10 seconds, and the distance covered (s) is 200 meters.
The formula for displacement (s) in terms of initial velocity (u), acceleration (a), and time (t) is:
s = ut + (1/2)at^2
Since the car starts from rest, its acceleration (a) will be equal to the average acceleration during the 10-second interval. Therefore, we need to find the acceleration first.
The formula for average acceleration (a_avg) in terms of initial and final velocities (u and v) and time (t) is:
a_avg = (v - u) / t
Here, the final velocity (v) can be determined using the formula:
v = u + at
Since the car started from rest, its final velocity will be equal to the average velocity (v_avg) during the 10-second interval. Therefore, we can write:
v_avg = (u + v) / 2
Now, let's find the acceleration (a):
a_avg = (v - u) / t a_avg = (v_avg - u) / t
We will substitute the given values:
u = 0 m/s (initial velocity) v_avg = 200 m / 10 s = 20 m/s (average velocity) t = 10 s (time)
a_avg = (20 - 0) / 10 a_avg = 2 m/s^2
Since we have now found the acceleration (a_avg), we can substitute it into the displacement formula:
s = ut + (1/2)at^2
s = 0 + (1/2)(2)(10^2) s = 0 + (1/2)(2)(100) s = 0 + (1/2)(200) s = 100 m
Therefore, the displacement of the car during the 10-second interval is 100 meters.