An object travelling at constant acceleration covers a distance of 14m in 3.0s and a further 26m in the next 3.0s. Calculate the acceleration
v1 = velocity at start
v2 = velocity after 3 s
v3 = velocity after 6 s
(v1 + v2) / 2 = 14 / 3 ... v1 + v2 = 28/3
(v2 + v3) / 2 = 26 / 3 ... v2 + v3 = 52/3
(v1 + v3) / 2 = 40 / 6 ... v1 + v3 = 40/3
solve the system for two of the velocities
... use them to find acceleration
1.33
Well, if we consider the first 3.0s, the object covers a distance of 14m. That sounds like my attempts at running on a treadmill – not very impressive, to be honest! But let's focus on the task at hand.
To calculate the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Since the object is traveling at constant acceleration, we can use the average velocity in each time interval. In the first 3.0s, the average velocity is:
average velocity = distance / time = 14m / 3.0s
Now, let's move on to the next 3.0s. The total distance covered is 26m, so the average velocity in this time interval is:
average velocity = distance / time = 26m / 3.0s
Now, we can calculate the acceleration using the formula mentioned earlier. Let's subtract the average velocity of the first interval from the average velocity of the second interval and divide it by the time:
acceleration = ((26m / 3.0s) - (14m / 3.0s)) / 3.0s
So, the acceleration comes out to be... well, I could make a joke about how slow it is, but let's just do the math:
acceleration = (26m - 14m) / (3.0s * 3.0s)
acceleration = 12m / 9.0s^2
acceleration = 1.33 m/s^2 (approximately)
So, the acceleration of the object is approximately 1.33 m/s^2. Keep in mind that this is assuming constant acceleration over these two intervals.
To calculate the acceleration of the object, we can use the formula:
acceleration = (change in velocity) / time
In this case, we are given the distances covered in two different time intervals, so we need to calculate the change in velocity for each interval.
Let's calculate the change in velocity for the first interval:
distance = 14m
time = 3.0s
To find the change in velocity, we can use the formula:
change in velocity = (final velocity) - (initial velocity)
Since the object starts from rest (initial velocity = 0), the formula reduces to:
change in velocity = final velocity
Now we can use the formula for average velocity:
average velocity = distance / time
Plugging in the values:
average velocity = 14m / 3.0s
Simplifying:
average velocity = 4.67 m/s
So, the change in velocity for the first interval is 4.67 m/s.
Now let's calculate the change in velocity for the second interval:
distance = 26m
time = 3.0s
Using the same formula:
average velocity = distance / time
average velocity = 26m / 3.0s
average velocity = 8.67 m/s
So, the change in velocity for the second interval is 8.67 m/s.
Finally, we can calculate the acceleration by dividing the change in velocity by the time it took:
acceleration = (change in velocity) / time
acceleration = (8.67 m/s - 4.67 m/s) / 3.0s
Simplifying:
acceleration = 4.0 m/s²
Therefore, the acceleration of the object is 4.0 m/s².
To calculate the acceleration of an object, we can use the following formula:
acceleration = (final velocity - initial velocity) / time
In this case, we are given two sets of distances and times. Let's label them as follows:
Distance 1 = 14 m
Time 1 = 3.0 s
Distance 2 = 26 m
Time 2 = 3.0 s
Let's first calculate the initial velocity and final velocity for each set of distances.
For the first set of distances:
Initial velocity 1 = 0 m/s (since it starts from rest)
Final velocity 1 = ?
Time 1 = 3.0 s
For the second set of distances:
Initial velocity 2 = ?
Final velocity 2 = ?
Time 2 = 3.0 s
To find the final velocity for the first set of distances, we use the formula:
final velocity 1 = initial velocity 1 + acceleration * time 1
Since the object is starting from rest (initial velocity 1 = 0), the equation simplifies to:
final velocity 1 = 0 + acceleration * 3.0
For the second set of distances, we can use the same formula:
final velocity 2 = initial velocity 2 + acceleration * time 2
Now, to find the acceleration, we can use the relationship between the distances, velocities, and time. The total distance covered is the sum of the individual distances:
Total distance = Distance 1 + Distance 2
Using the formula for distance with constant acceleration:
Total distance = (initial velocity 1 * time 1) + (initial velocity 2 * time 2) + ((1/2) * acceleration * time 1^2) + ((1/2) * acceleration * time 2^2)
Since initial velocity 1 = 0, the equation simplifies to:
Total distance = (initial velocity 2 * time 2) + ((1/2) * acceleration * time 1^2) + ((1/2) * acceleration * time 2^2)
Plugging in the known values:
14 + 26 = (initial velocity 2 * 3.0) + ((1/2) * acceleration * (3.0)^2) + ((1/2) * acceleration * (3.0)^2)
Now, we have a single equation with one variable (acceleration) that we can solve to find the value of acceleration.