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

[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.

 

[STAii]

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 ).
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=(v_f-v_i)/t
This is the definition of average acceleration, where v_f is the final velocity, v_i 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=v_it + 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.

 

[hims100]

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