Q11.The table below shows how the braking distance x for a car depends on its initial speed u.
| u / ms-1 | 5 | 10 | 20 | 40 |
| X / M | 2 | 8 | 32 | 128 |
The relationship between x and u is: doubling speed increases distance by a factor of 4.
i)The reaction time of a driver is 0.60s. Calculate the stopping distance of the car when u is 30ms-1.
Thinking distance= 18m
and i didn't know how to work out braking distance so i looked at the mark scheme to get this number
so braking distance=72m
then i used this number to get the stoppign distance and got:
stopping idstamce=
18m + 72m = 90m stopping distance.
Please show mehow to work out braking distance for this questions, show where you got numbersfrom, what equations used and full wqriting not jut symbols please/
by the way for the table
5 is above 2
10 is above 8
and so on
the space i left aren't posted/shown
I reposted like you asked and i included the full question and my working out and what i need help with so pplease help
To calculate the braking distance for the given table, we need to determine the relationship between x (braking distance) and u (initial speed). By observing the table, we can see that doubling the speed (u) increases the braking distance (x) by a factor of 4.
i) The formula for calculating the total stopping distance is the sum of the thinking distance and the braking distance.
Thinking distance: Given a reaction time of 0.60s, we can calculate the thinking distance using the formula:
Thinking distance = u × reaction time
Substituting the given values:
u = 30 m/s
Reaction time = 0.60s
Thinking distance = 30 m/s × 0.60s = 18m
(ii) Now, let's calculate the braking distance:
From the table, we can see that when the initial speed is 20m/s, the braking distance is 32m. To determine the relationship between x and u, we can see that when the initial speed is doubled, the braking distance is quadrupled.
So, we can set up a proportion to find the braking distance for an initial speed of 30 m/s:
(previous braking distance) 32m / 20m/s = (new braking distance) x / 30m/s
Using the proportion, we can solve for x:
x = (32m / 20m/s) × 30m/s
x ≈ 48m
Therefore, the braking distance (x) for an initial speed of 30 m/s is approximately 48m.
(iii) Finally, the total stopping distance is obtained by adding the thinking distance to the braking distance:
Total stopping distance = Thinking distance + Braking distance
Total stopping distance = 18m + 48m
Total stopping distance ≈ 66m
Thus, the total stopping distance for a car with an initial speed of 30 m/s is approximately 66m.