Question

Please answer all parts to question and provide explanation if needed.

a) If you only have random error what's the percentage that the true value will lie between L + standdevation of L, and L - standarddeviation of L

b) How can you get the velocity from the distance curve?

c) How can you get the Distance from the velocity curve?

d)Potential Energy is the energy of position

Kinetic Energy is the energy of movement

So is Force * distance equal to which of the two?

e) Energy cannot be created or destroyed only transformed. With that in mind, the bulk of energy is lost to the system in this form. What is this form?

Answer 1

If v(t) is the velocity at time t, the distance traveled from time t1 to time t2 is the area under the graph of v(t) from t=t1 to t=t2. This may have to be done by evaluating the integral of v(t) dt from t1 to t2.

Some areas may be a shape whose area is easy to compute from a simple formula.

For example, suppose v(t) = 3t + 5 and you want to find the distance traveled from t=2 to t=7. The area under the graph is going to be a trapezoid with vertical parallel bases. The bases of the trapezoid are v(2) = 11 and v(7) = 26. The height of the trapezoid is 7 - 2 = 5. The area of the trapezoid is 1/2 (11+ 26) (5) = 92.5 which is the distance traveled. Remember to attach the proper units of measurement. If velocity is meters per second and time is seconds, the distance is meters.

Answer 2

Answer a:

It depends on the L value. No classification of the value of L. For random error if L is large then the percentage will be more than 95%.

Answer b:

On a graph, the line which rises in equal proportion with vertical and horizontal scale is called a gradient of the graph.

When the distance-time graph is plotted. The gradient obtained is speed but not velocity because the distance is the scalar quantity.

When a graph is plotted as displacement versus time then the gradient obtained is velocity since displacement and velocity are both vector quantities.

Hence, on obtaining the gradient. The speed value can be obtained.

In order to find the velocity, instead of plotting distance-time graph, plot displacement time graph. Below are the figures describing the motion of the distance-time graph.

Answer c:

On a speed-time graph, the area under the line is numerically equal to the distance travelled.

One of the examples is given below:

Answer d:

The total energy is the addition of potential energy and kinetic energy. Thus the,

work done = energy transformed

Hence, the Force*distance moved is equal to the transformation energy taking place from potential to kinetic energy.

For example, if the potential energy(50 J) is converted to kinetic energy(50 J) then the value remains the same.

Hence, energy = force*distance moved

Answer e:

According to the law of conservation of energy, energy cannot be created nor be destroyed. It changes from one form to another. Hence, the energy lost to surrounding is mainly thermal energy.