... One car accelerates at 3.5 m/s^2 the other accelerates at 6.5 m/ s^2. Where do they hit if the initial velocity is 0 for both cars?
Answers (1)
Ok, you are given acceleration and you know that speed equals acceleration times time, and distance equals speed times time. So distance equals acceleration times time squared. So you can write an equation for that.
d = at^2
For the first car:
d = 3.5 m/s^2 x t^2
For the second car, d is given 300 m and acceleration is negative, so:
d = 300m - 6.5 m/s^2 x t^2
We put the units into the equations because they can be treated as fractions to be sure they cancel and leave the answer in the units we want. Next, d is the same for both equations, so we set the two equations equal:
3.5 m/s^2 x t^2 = 300m - 6.5 m/s^2 x t^2 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Add 6.5 m/s^2 x t^2.
10 m/s^2 x t^2 = 300m Divide by 10 m/s^2.
t^2 = 30 s^2 Did you notice how the m above the bar cancels the m below? That's why we do it this way. If you didn't have the units in there, you would be totally bewildered right now.
t = √(30 s^2) = 5.477 s Now you put this into either original equation to find the distance.