1) A car, initially traveling with a uniform velocity, accelerates at a rate of 1.0 m/s2 for a period of 12.0 seconds. If the car traveled 190.0 m during this 12.0 second period, what was the velocity of the car when it started to accelerate?
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To determine the initial velocity of the car, we can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the car initially traveled with a uniform velocity, so its final velocity is the same as the initial velocity (v = u). The car then accelerates at a rate of 1.0 m/s² for a period of 12.0 seconds.
We are given that the car traveled a distance of 190.0 m during this 12.0 second period, so we can use the formula:
s = ut + (1/2)at²
where:
s = distance
u = initial velocity
t = time
a = acceleration
Rearranging the formula to solve for the initial velocity (u):
u = (2s - at²) / (2t)
Plugging in the values we have:
u = (2 * 190.0 m - 1.0 m/s² * (12.0 s)²) / (2 * 12.0 s)
Now we can calculate the initial velocity:
u = (380.0 m - 1.0 m/s² * (144.0 s²)) / 24.0 s
u = (380.0 m - 144.0 m/s²) / 24.0 s
u = 236.0 m / 24.0 s
u ≈ 9.83 m/s
Therefore, the velocity of the car when it started to accelerate was approximately 9.83 m/s.