Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

When deciding how many significant figures your answer should have, base it off the given value with the fewest significant figures. In this case, the velocity has two significant figures and the time has three; therefore, our answer should have only two significant figures in order to match the least precise given value (velocity).

We can calculate our answer using the formula for velocity.

Rounded to two significant figures, we can say that the car travels .

Torque is a force times the radius of the circle, given by the formula:

In this case, we are given the radius in centimeters, so be sure to convert to meters:

Use this radius and the given force to solve for the torque.

If the see-saw is  in total, then it has  on either side of the fulcrum. 

The question is asking us to find the equilibrium point; that means we want the net torque to equal zero.

Now, find the torque for the first child.

We are going to use the force of gravity for the force of the child.

When thinking of torque, treat the positive/negative as being clockwise vs. counter-clockwise instead of up vs. down. In this case, child one is generating counter-clockwise torque. That means that since , child two will be generating clockwise torque.

Solve for the radius (distance) of the second child.

The formula for torque is:

In this formula,  is the angle the force makes with the lever arm. Since our force is applied perpendicularly, this angle will be . Use this angle, the force applied, and the length of the lever arm to calculate the torque.

We know that the system will be in equilibrium at the final point, meaning that the final net torque must be zero. That means that the torque generated by the boulder and the torque generated by the construction worker should be equal.

The negative sign is due to the placement of the two masses on opposite sides of the fulcrum. Essentially, one mass will have a positive radius and the other will have a negative radius. Use the definition of torque to expand this equation.

In this case, the forces will be the weights of the two objects due to gravity.

We can cancel the acceleration due to gravity from the equation to simplify.

Using the given information from the question, we can solve for the distance between the worker and the fulcrum. We know the mass of the worker, the mass of the boulder, and the distance between the boulder and the fulcrum.

Knowns:

Unknowns:

 that Trevor actually travels = ?

Equation:

Since Trevor takes a moment to react before stepping on the breaks, determine how far Trevor travels during the reaction time. At this time he is traveling at a constant velocity.

Next, using kinematic equations to determine where Trevor stops his car based on the acceleration of his car.

 beyond the reaction point

Total distance traveled is the reaction time distance plus the distance traveled during the deceleration period.

total distance traveled 

To find the distance beyond the red light, subtract the distance traveled from the distance to the light

distance beyond red light 

Knowns:

Unknowns:

Equation:

To make things easier, set the frame of reference to the police officer.  This means that the police officer is traveling at 0km/h and the speeder is moving at a speed relative to the officer.

So the new relative velocities are:

This will help make the math easier.

Convert the relative velocity of the speeder to m/s.

Now there are two equations that have to be true for the officer to catch up to the speeder.

There are two things that connect these equations.  First, the distance that the officer travels and the speeder travels must be the same.  Additionally the final velocity of both the officer and the speeder must be the same.

Rearrange the speeder equation for the distance traveled.

Set the two equations equal, as the distance traveled of the speeder is equal to the distance traveled by the officer.

Remember that the reference point is at the officer’s perspective so the officer has an initial velocity of 0m/s.

Rewrite the equation breaking up the change of time into time final and time initial.

Distribute on the left side.

Substitute values

Simplify

Remember that the final time for both the officer and the speeder are the same.  So rearrange this in the form of a quadratic equation.

Use the quadratic formula to solve.  

Possible answers:  or 

Since the officer did not move until , then the second answer must be correct.

We are given final velocity and we know initial velocity is 0. We can use the following kinematics formula to relate final speed, initial speed, acceleration, and displacement:

The initial velocity is zero since Usain starts from rest. Therefore we can remove it from the equation.

Rearrange the equation to solve for acceleration.

Knowns:

Unknowns:

Equation:

First we need to determine Peter’s acceleration. The best kinematic equation to use here is:

Once Peter’s acceleration is known it is possible to find the distance he traveled.

Peter’s initial velocity is  so this equation simplifies to