# Uniform Aceleration: Speed of Car at End of Braking Period

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"A car accelerates from rest and travels for 4.98 s with a uniform acceleration of +1.50 m/s^2. The driver then applies the brakes, causing a uniform acceleration of -1.99 m/s^2. If the brakes are applied for 3.06s, how fast is the car going at the end of the braking period? And how far has the car gone?"

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Solution. By the hypothesis, the initial speed of the car is v0=0, and the uniform acceleration a1=1.5m/s^2. So, after t1=4.98s, the speed of the car V is

V=a1*t1=4.98*1.5=7.47 (m/s).

The direction of V is the same as the acceleration, say "right".

Then, the driver applies the brakes, causing a uniform acceleration of a2=-1.99m/s^. The "-" means decreasing ...

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- BSc , Wuhan Univ. China
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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