a car travels on a straight road.
a) starting from rest, the car is going 44 ft/s (30 mi/h) at the end of 5.0 s. What is the car's average acceleration in ft/s^2
b) in 4.0 more seconds, the car is going 88 ft/s (60 mi/h). what is the car's average acceleration for this time period?
c) the car then slows to 66 ft/s (45 mi/h) in 3.0 s. what is the average acceleration for this time period?
d) what is the overall average acceleration for the total time?
a = change in velocity/change in time
= 44/5 = 8.8 ft/s^2
a = same formula = (88-44)/4 = 11 ft/s^2
a = (66 -88)/3 = -7.33 ft/s^2
sum of a*t / total t
(8.8*5 + 11*4 - 7.33*3)/12
= 5.5 m/s^2
How to solve
a) To find the average acceleration, we can use the formula:
average acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 ft/s
Final velocity (v) = 44 ft/s
Time (t) = 5.0 s
Substituting the values into the formula, we get:
average acceleration = (44 ft/s - 0 ft/s) / 5.0 s
average acceleration = 44 ft/s / 5.0 s
average acceleration = 8.8 ft/s^2
Therefore, the car's average acceleration is 8.8 ft/s^2.
b) To find the average acceleration, we will use the same formula:
average acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 44 ft/s
Final velocity (v) = 88 ft/s
Time (t) = 4.0 s
Substituting the values into the formula, we get:
average acceleration = (88 ft/s - 44 ft/s) / 4.0 s
average acceleration = 44 ft/s / 4.0 s
average acceleration = 11 ft/s^2
Therefore, the car's average acceleration for this time period is 11 ft/s^2.
c) Similarly, to find the average acceleration, we will use the same formula:
average acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 88 ft/s
Final velocity (v) = 66 ft/s
Time (t) = 3.0 s
Substituting the values into the formula, we get:
average acceleration = (66 ft/s - 88 ft/s) / 3.0 s
average acceleration = -22 ft/s / 3.0 s
average acceleration = -7.33 ft/s^2
Since the velocity is decreasing, the acceleration is negative. Therefore, the car's average acceleration for this time period is -7.33 ft/s^2.
d) To find the overall average acceleration, we need to consider the total time and the total change in velocity. In this case, the total time is 5.0 s + 4.0 s + 3.0 s = 12.0 s. The total change in velocity is 66 ft/s - 0 ft/s = 66 ft/s.
Using the formula:
average acceleration = (final velocity - initial velocity) / time
average acceleration = (66 ft/s - 0 ft/s) / 12.0 s
average acceleration = 66 ft/s / 12.0 s
average acceleration = 5.5 ft/s^2
Therefore, the overall average acceleration for the total time is 5.5 ft/s^2.
To find the average acceleration, we use the formula:
Average acceleration (a) = (final velocity - initial velocity) / time
Let's calculate the answers to each of the questions step by step:
a) Given:
Initial velocity (u) = 0 ft/s (starting from rest)
Final velocity (v) = 44 ft/s
Time (t) = 5.0 seconds
Using the formula, we get:
Average acceleration (a) = (44 ft/s - 0 ft/s) / 5.0 s
= 44 ft/s / 5.0 s
= 8.8 ft/s^2
So, the car's average acceleration for this time period is 8.8 ft/s^2.
b) Given:
Initial velocity (u) = 44 ft/s
Final velocity (v) = 88 ft/s
Time (t) = 4.0 seconds
Using the formula, we get:
Average acceleration (a) = (88 ft/s - 44 ft/s) / 4.0 s
= 44 ft/s / 4.0 s
= 11 ft/s^2
So, the car's average acceleration for this time period is 11 ft/s^2.
c) Given:
Initial velocity (u) = 88 ft/s
Final velocity (v) = 66 ft/s
Time (t) = 3.0 seconds
Using the formula, we get:
Average acceleration (a) = (66 ft/s - 88 ft/s) / 3.0 s
= -22 ft/s / 3.0 s
= -7.33 ft/s^2
Note: The negative sign indicates that the car is slowing down.
So, the car's average acceleration for this time period is -7.33 ft/s^2.
d) To find the overall average acceleration for the total time, we first need to calculate the total change in velocity and the total time.
The total change in velocity is the final velocity minus the initial velocity:
Total change in velocity = 66 ft/s - 0 ft/s = 66 ft/s
The total time is the sum of the individual times:
Total time = 5.0 s + 4.0 s + 3.0 s = 12.0 seconds
Using the formula, we get:
Overall average acceleration = Total change in velocity / Total time
= 66 ft/s / 12.0 s
= 5.5 ft/s^2
So, the overall average acceleration for the total time is 5.5 ft/s^2.