Question: What is the acceleration of a body moving with constant acceleration?

In summary, the conversation discusses two different problems involving motion and acceleration. The first problem asks for the initial velocity and acceleration of a body based on given distances traveled in the first and third seconds. The second problem involves calculating the spacecraft's average acceleration while its rocket motors are firing, and the distance traveled by the spacecraft in the first 10 seconds after the motors are started. The conversation includes equations and explanations for solving these problems and clarifies a mistake in the distance calculation for the second problem.
  • #1
hims100
Hi all,
I came across few questions in motion.Can anyone can help me out in this.
Q1)A body moving with a constant acceleration travels the distances 3m and 7m respectively in the first and third seconds. Calculate :
(i)initial velocity
(ii)the acceleration of body

Q2)A spacecraft flying in a straight course at 75 km/sec fires its rocket motors for 6 seconds. At the end of this time its speed is 120 km/sec in the same direction. Find :
(i)the spacecraft s average acceleration while the motors were firing.
(ii)the distance traveled the spacecraft in the first 10 seconds after the rocket motors were started, the motors having been in action for only 6 seconds.
 
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  • #2
Hello hims100, and welcome to the forums.
Q1
You can derive an equation that gives you the distance traveled by a certain object in a certain second, i derived it for you, and here it goes (if you want to know how it was derived, just ask :smile:).
S=v0 + a(n-0.5)
Where S stands for the displacement in a certain second, v0 stands for the initial velocity, and (a) stands for the acceleration, (n) stands for the number of the second in subject.
Now you know S in the is the first second, and you also know S in the third second, so you can apply the above eqauation, and solve for the unknowns (a) and v0
(if you are having trouble making this, tell us, we will help).

Q2
a=(vf-vi)/t
This is the definition of average acceleration, where vf is the final velocity, vi is the initial velocity, and (t) is the time in which the acceleration happened.
Now apply the equation on the givings of the problem
a = (120-75)/6 = 7.5 m/s2
So now you have the acceleration ready for use.

S=vit + 0.5at2
Use this equation to find the distance made by the rocket for a certain amount of time (t).
For example, to find the distance made by the rocket in the first 10 seconds (t=10s)
S = 75*10 + 0.5*7.5*102
S = 750 + 375
S = 1125 m

You can do the same to find the distance made by the rocket in the first 6 seconds (put 6 instead of 10 in the value of t).

I hope i helped.
 
  • #3
Hi,
Thanks a lot. The solution provided worked.However, still one problem is there as given below :

Q2
a=(vf-vi)/t
This is the definition of average acceleration, where vf is the final velocity, vi is the initial velocity, and (t) is the time in which the acceleration happened.
Now apply the equation on the givings of the problem
a = (120-75)/6 = 7.5 m/s2
So now you have the acceleration ready for use.
AVERAGE ACCELERATION IS CORRECT.

S=vit + 0.5at2
Use this equation to find the distance made by the rocket for a certain amount of time (t).
For example, to find the distance made by the rocket in the first 10 seconds (t=10s)
S = 75*10 + 0.5*7.5*102
S = 750 + 375
S = 1125 m

THE DISTANCE TRAVELLED IS INCORRECT. THE ANSWER TO THIS PROBLEM IS 1065 KM.

You can do the same to find the distance made by the rocket in the first 6 seconds (put 6 instead of 10 in the value of t).

I hope i helped.

THANKING IN ANTICIPATION
 

1. What is acceleration?

Acceleration is a measure of how much an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, it is the rate at which an object's speed or direction changes.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it took for that change to occur. The formula for acceleration is: a = (v2-v1)/t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

3. What is constant acceleration?

Constant acceleration occurs when an object's velocity changes at a constant rate over time. This means that the object's acceleration remains the same throughout its motion. An example of constant acceleration is an object falling under the influence of gravity.

4. How is constant acceleration different from variable acceleration?

As the name suggests, constant acceleration remains the same throughout an object's motion, while variable acceleration can change at different points in time. This means that an object with variable acceleration will have a changing rate of change in its velocity, while an object with constant acceleration will have a consistent rate of change.

5. Can an object have constant acceleration and changing velocity?

Yes, an object can have constant acceleration and still have a changing velocity. This occurs when the direction of the object's motion changes while its acceleration remains constant. An example of this is circular motion, where an object's velocity is constantly changing due to its changing direction of motion.

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