Object travels 22.5 m in the eighth second with uniform acceleration

[einstein101]

Homework Statement

An object that is acclerating uniformly travels 22.5 m in the eighth second of its motion.
a) what is the acceleration of the object?

b) how far does the object travel in 6 seconds?

Homework Equations

I'm not exactly sure what equation would be necessary-
perhaps -- a=v-u/t
v=u+at
x=ut+1/2at^2

The Attempt at a Solution

i attempted to use the a=v-u/t equation, however, it wasn't successful. I don't even think you can use that equation since we don't have the values for velocity;initial nor final.

 

[PhanthomJay]

The object has no motion at t = 0. How far does it travel in 8 seconds? How far does it travel in 7 seconds? Its displacement between the. 7th and 8th seconds is given as 22.5 m. Use your last equation.

 

[NascentOxygen]

Hi einstein101. The eighth second is that time difference between seven seconds and eight seconds.

travel during first 7 seconds= u.7 + (1/2)a.7²

travel during first 8 seconds= ?

 

[einstein101]

But how do I find the initial velocity for the equation?
And how would I exactly go about finding the acceleration?

 

[e^(i Pi)+1=0]

The object has no motion at t = 0. How far does it travel in 8 seconds? How far does it travel in 7 seconds? Its displacement between the. 7th and 8th seconds is given as 22.5 m. Use your last equation.

It says nowhere that the object started from rest.

 

[Doc Al]

It says nowhere that the object started from rest.

It says "in the eighth second of its motion". I would interpret that to mean that it started from rest.

 

[NascentOxygen]

But how do I find the initial velocity for the equation?
And how would I exactly go about finding the acceleration?

Can you finish the equation I left uncompleted?

 

[e^(i Pi)+1=0]

It says "in the eighth second of its motion". I would interpret that to mean that it started from rest.

Hmm, I suppose you're right.

 

[einstein101]

so travel during first 8 seconds=u x 8 +1/2(a)(8)^2

then what do i do?

 

[NascentOxygen]

so travel during first 8 seconds=u x 8 +1/2(a)(8)^2

then what do i do?

Good. Now subtract that from the companion equation I gave you, viz., of distance traveled during first 7 seconds.

 

[PhanthomJay]

so travel during first 8 seconds=u x 8 +1/2(a)(8)^2

then what do i do?

It has been established that the object starts from rest and thus u = 0 and the distance traveled in 8 seconds is 32(a). In a similar manner, find the distance traveled in 7 seconds. Subtract this 2nd equation from the first equation and set the result equal to 22.5 to solve for a.