If a car at rest accelerates uniformly to a speed of 40 m/s in 20 seconds, it covers a distance of
Question
If a car at rest accelerates uniformly to a speed of 40 m/s in 20 seconds, it covers a distance of
Solution
To find the distance covered by the car, we can use the formula for distance covered under uniform acceleration, which is:
d = ut + 0.5at^2
where:
- d is the distance covered,
- u is the initial speed,
- a is the acceleration, and
- t is the time.
Given that the car starts from rest, u = 0. The final speed v = 40 m/s and the time t = 20 s.
First, we need to find the acceleration a. We can use the formula for acceleration, which is:
a = (v - u) / t
Substituting the given values:
a = (40 m/s - 0) / 20 s = 2 m/s^2
Now we can substitute u = 0, a = 2 m/s^2, and t = 20 s into the formula for distance:
d = 0 + 0.5 * 2 m/s^2 * (20 s)^2 = 0.5 * 2 m/s^2 * 400 s^2 = 400 m
So, the car covers a distance of 400 meters.
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