A car that starts from rest and has uniform acceleration. The car must travel 60 meters before reaching a speed of 10 m/s. What total distance must the car travel in order to reach a speed of 30 m/s?
average speed for 60 m is ... (0 + 10) / 2 = 5 m/s
... so travel time is ... 60 / 5 = 12 s
... and acceleration is ... 10 m/s / 12 s = 5/6 m/s^2
time to reach 30 m/s ... 30 / 5/6 = 36 s
... average speed is ... (0 + 30) / 2 = 15 m/s
... distance is ... 36 s * 15 m/s = 540 m
with uniform acceleration ... d = 1/2 a t^2
... the distance is proportional to the square of the time
... three times the time means nine times the distance
To find the total distance the car must travel to reach a speed of 30 m/s, we need to use the equations of motion.
We know that the initial velocity, u, is 0 m/s (car starts from rest).
We also know the final velocity, v, is 30 m/s.
Let's denote the acceleration as a and the total distance as d.
The first step is to find the acceleration (a) using the information given in the problem.
We can rearrange the second equation of motion, v^2 = u^2 + 2as, to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (30^2 - 0^2) / (2 * 60)
a = 900 / 120
a = 7.5 m/s^2
Now we can use the third equation of motion, v^2 = u^2 + 2as, to find the total distance (d) the car must travel to reach a speed of 30 m/s.
d = (v^2 - u^2) / (2a)
Substituting the values:
d = (30^2 - 0^2) / (2 * 7.5)
d = 900 / 15
d = 60 meters
Therefore, the total distance the car must travel to reach a speed of 30 m/s is 60 meters.
To find out the total distance the car must travel in order to reach a speed of 30 m/s, we can use the equations of motion. The equation that relates distance (d), initial velocity (u), final velocity (v), and acceleration (a) is:
v^2 = u^2 + 2ad
Given that the car starts from rest (u = 0), accelerates uniformly, and travels 60 meters before reaching a speed of 10 m/s (v = 10 m/s), we can rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2d)
= (10^2 - 0^2) / (2 * 60)
= 100 / 120
= 5/6 m/s^2
Once we have the acceleration, we can use the equation of motion to find the total distance (D) required to reach a final velocity (V) of 30 m/s:
V^2 = u^2 + 2aD
Rearranging the equation to solve for D, we get:
D = (V^2 - u^2) / (2a)
= (30^2 - 0^2) / (2 * 5/6)
= 900 / (10/6)
= 900 * 6/10
= 540 meters
Therefore, the car must travel a total distance of 540 meters in order to reach a speed of 30 m/s.