A speedboat increases in speed from 20 m/s to 30 m/s in a distance of 200m. Find (a) the magnitude of its acceleration and (b) the time it takes the boat to travel this distance.
(a) (I am not sure what the magnitude is)
(b) 200m x s/30m = 6.67s (is this correct?)
It's a bit easier if you do (b) first.
(b) The average speed will be 25 m/s, and the time required to travel that distance will be 200 m/(average speed) = 200m/(25 m/s) = 8 s
(a) The magnitude of the acceleration is (speed change)/time = (10 m/s)/8 s = 1.25 m/s^2
You could also have used the formula
2aX = V2^2 - V1^2 = 900 - 400 = 500, and solved for the acceleration
a = 500/(2X) = (500 m^2/s^2)/400 m. You'd get the same answer; however, that formula is a bit harder to remember.
1,25
(a) The magnitude of acceleration (a) can be calculated using the formula:
a = (final velocity - initial velocity) / time
Substituting the given values:
a = (30 m/s - 20 m/s) / t
Since the initial velocity (u) is 20 m/s and the final velocity (v) is 30 m/s, the formula becomes:
a = (30 m/s - 20 m/s) / t
a = 10 m/s / t
Therefore, the magnitude of acceleration is 10 m/s divided by the time (t) taken.
(b) To find the time it takes for the boat to travel a distance of 200m, we can rearrange the formula:
distance = (initial velocity + final velocity) / 2 * time
Substituting the given values:
200m = (20 m/s + 30 m/s) / 2 * t
Simplifying further:
200m = 50 m/s / 2 * t
200m = 25 m/s * t
Dividing both sides by 25 m/s, we get:
t = 200m / 25 m/s
So, the time it takes the boat to travel a distance of 200m is 8 seconds.
(a) The magnitude of acceleration can be calculated using the formula:
acceleration = change in velocity / time
The change in velocity is the difference between the final velocity and the initial velocity:
change in velocity = final velocity - initial velocity
In this case, the final velocity is 30 m/s and the initial velocity is 20 m/s. Therefore:
change in velocity = 30 m/s - 20 m/s = 10 m/s
Now, we can calculate the magnitude of acceleration:
acceleration = change in velocity / time
(b) Your calculation for the time it takes the boat to travel the distance is correct. The formula you used is:
time = distance / speed
In this case, the distance is 200 m and the speed is 30 m/s. Therefore:
time = 200 m / 30 m/s = 6.67 s
(a) The magnitude of acceleration can be calculated using the formula:
acceleration = (change in velocity) / time
In this case, the change in velocity is 30 m/s - 20 m/s = 10 m/s, and we need to find the time it takes for this change to occur.
(b) To find the time it takes for the boat to travel a distance of 200 m, we can use the formula:
time = distance / speed
Using the given values, we have:
time = 200 m / 30 m/s = 6.67 s
So, your calculation for the time it takes the boat to travel this distance is correct.
Therefore, the answers are:
(a) The magnitude of acceleration is 10 m/s^2.
(b) The time it takes the boat to travel this distance is 6.67 seconds.