An object at rest accelerates through a distance of 1.5 m at which point the instantaneous velocity of the object is 3.5m/s. Determine:
a. The average acceleration of the object
b. The time it took the object to travel 1.5m
c. The average velocity of the object during this period of motion
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To answer these questions, we can use the equations of motion that relate distance, velocity, acceleration, and time. Specifically, we can use the following equations:
1. v = u + at
2. s = ut + (1/2)at^2
3. v^2 = u^2 + 2as
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the distance
- t is the time
a. The average acceleration of the object:
The average acceleration of the object can be calculated using the equation:
average acceleration = change in velocity / time interval
We know that the object's initial velocity is zero because it starts from rest. The final velocity is given as 3.5 m/s. As a result, the change in velocity is 3.5 m/s - 0 m/s, which gives us a change in velocity of 3.5 m/s.
To find the time interval, we need to use the second equation of motion. As we are given the distance traveled as 1.5 m, we can rearrange the equation as follows:
s = ut + (1/2)at^2
1.5 = 0*t + (1/2)a*t^2
1.5 = (1/2)a*t^2
Since we only have one equation with two unknowns (a and t^2), we need more information. Without further information, we cannot determine the average acceleration of the object.
b. The time it took the object to travel 1.5 m:
To find the time it took the object to travel 1.5 m, we can rearrange the second equation of motion:
s = ut + (1/2)at^2
1.5 = 0*t + (1/2)a*t^2
Again, we don't have enough information to solve for the time because we don't know the acceleration.
c. The average velocity of the object during this period of motion:
The average velocity of the object can be calculated using the equation:
average velocity = total distance / total time
Since we are given that the object travels a distance of 1.5 m, we need to determine the total time it took to travel that distance. Without knowing the acceleration or the time, we cannot calculate the average velocity.