Solving for Work Done When Accelerating a Mass

[Jay529]

Homework Statement

Need help checking my work and appropriate use of equations.

Relevant Equations

acceleration: s=ut + 1/2 ut^2, final velocity: V= u+at, work done: W=1/2 mv^2

I wanted to make sure these were the correct equations to use for they were not given. I had to research to get this far and only had the below statement to go off.

The problem is an object with initial velocity = "0." It travels 0.495m in 0.1625sec and weights 8.4 kg
or
Initial velocity (u) = 0 m/s, Mass (m) = 8.4 kg, Distance (s) = 0.495 m, Time (t) = 0.1625

Solving for acceleration: 0.495 = 0 + 1/2 * a (0.1625)^2
a= (2*0.495)/ 0.1625^2 = 37.495m/sec^2

Now that I have acceleration
Calculate final velocity: V= 37.495 * .01625 = 6.09375m/s

Solving for Work done: W=1/2 * 8.4 * 6.09375^2 = .5 * 8.4 * 37.125 = 155.925 joules

 

[haruspex]

You are assuming constant acceleration. Is that given?

 

[Jay529]

You are assuming constant acceleration. Is that given?

Yes, I believe.

 

[haruspex]

Yes, I believe.

Then I get the same result to four significant figures. The mass is only given to two significant figures, so really that is all you can give in the answer.
Had you worked algebraically you would have got some cancellation: $2m(\frac st)^2$. That allows you to check that the result is dimensionally correct and can improve accuracy. It has many other advantages. It is certainly easier for others to follow.

Btw, if the acceleration pattern can be anything you choose, the motion can be achieved using a quarter of the work.