Physics help!! *Velocity*?
*A car is traveling downhill, assuming no the angles of the hill is the same all the way down.*
If it takes 3s for a car to travel from 0-10m/s (velocity) how long will it take to travel double that, triple that?
I think 3 seconds each time it idk why. Or it takes less time to double and even less time to triple because it's going on a hill and it goes slow in the first half then faster in the second half so if it's goig faster won't it the velocity b bigger?
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Since the angle is the same, the acceleration is constant. Let’s use the following equation to determine the car’s acceleration.
vf = vi + a * t
10 = a * 3
a = 3⅓ m/s
For the next two questions, I believe that we are doubling and tripling the final velocity.
20 = 3⅓ * t
t = 20 ÷ 3⅓ = 6 seconds
30 = 20 ÷ 3⅓ = 9 seconds
In general we have V(t) = U(t) + Adt; where A = 10/3 m/s^2 is the constant acceleration downhill.
In the first dt = 3 seconds we have V(3) = 0 + 10/3*3 = 10 m/s.
Assuming we're now at U(3) = 10 m/s, we have V(t) = U(3) + A dt = 2 U(3); so we solve for dt = U(3)/A = 10*3/10 = 3 seconds. ANS when doubled.
Similarly U(6) = 20 m/s; so V(t) = U(6) + A dt = 3 U(3); so we have dt = (30 - 20)/(10/3) = 3 seconds. ANS when tripled.
By induction we can state that the speed will increase by one fold for each ten seconds of acceleration.
Cannot tell what grade you are in but if we assume "car traveling" means it is just coasting (motor not on) and ignore friction then the force making the car go faster is just gravity. With gravity F=mg where g is the acceleration of gravity. The kinematic equation Vf = Vi+ gt is the one we use here. you can see that velocity increases LINEARLY with the acceleration g. so if it gains 10m/s in the first 3 seconds it will also gain the same amount in the next 3 seconds.
Let me know thru comments if you have trouble with this.