1) A car is traveling down the interstate at 37.1 m/s. The driver sees a cop and quickly slows down. If the driver slows to 29.8 m/s in 3 seconds, what is the acceleration of the car?

2) While cleaning you lift an 87.3 N box up to a shelf that is 2.04 m above the ground. How much work was done on the box?

3) A child runs up the stairs and does 1250 J of work. If the child generates 267 W of power how long did it take for the child to run up the stairs?

4) A 8.642 kg rabbit is running across your back yard. If that rabbit has 125.6 J of Kinetic Energy, how fast is it running?

5) When using a simple machine you do 120 J of work on the machine. You notice that the machine gives you an output of 93 J. What is the efficiency of this machine?

6) A 212 kg bumper car is traveling 8.00 m/s when it rear ends a second 196 kg bumper car traveling 6.75 m/s. If the cars get stuck together, how fast are they traveling after the collision?

7) A wave is traveling through a string. If the wave has a wavelength of .23 m and a frequency of 12 Hz, what is the speed of the wave?

8) Find the wavelength of blue light if its frequency is 6.2 × 1014 Hz. (Hint: Remember the speed of light)

9) The speed of sound in air is about 343 m/s. If you scream and a friend hears you 0.287 s later, how far away from you is your friend?

1)

The acceleration of the car is the rate of change of velocity of the car; it can be calculated as:

where

u is the initial velocity

v is the final velocity

t is the time taken for the velocity of the car to change from u to v

In this problem, for this car we have:

u = 37.1 m/s

v = 29.8 m/s

t = 3 s

So, the acceleration is:

2)

The work done in lifting the box is equal to the potential energy transferred to the box during the process; it is given by:

where

F is the force applied

d is the displacement of the box

Here we have:

F = 87.3 N is the force applied

d = 2.04 m is the displacement of the box

So, the work done to lift the box is:

3)

The power is the rate of work done per unit time. It is calculated as:

where

W is the work done

t is the time taken to do the work

For the child in this problem, we have:

W = 1250 J is the work done by the child running up the stairs

P = 267 W is the power used

Therefore, re-arranging the equation, we find the time taken:

4)

The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by

where

m is the mass of the object

v is its speed

For the rabbit in this problem, we have:

m = 8.642 kg is the mass of the rabbit

KE = 125.6 is its kinetic energy

Solving the formula for v, we find the speed of the rabbit:

5)

The efficiency of a machine is the ratio between the energy produced in output by the machine and the work done in input. Mathematically, it is given by

where

is the energy in output

is the work in input

For the machine in this problem,

is the work in input

is the energy in output

Therefore, the efficiency of this machine is:

6)

During a collision, the total momentum of the system is always conserved before and after the collision. So we can write:

where

is the mass of the first car

is the initial velocity of the first car

is the mass of the 2nd car

is the initial velocity of the 2nd car

is the final velocity of the two cars stuck together (after the collision, they move together)

Solving the equation for v, we find:

7)

The relationship between speed, frequency and wavelength of a wave is given by the wave equation:

where

v is the speed of the wave

f is the frequency of the wave

is the wavelength

For the wave in the string in this problem we have:

(wavelength)

f = 12 Hz (frequency)

So, the speed of the wave is:

8)

The relationship between frequency and wavelength for an electromagnetic wave is given by

where:

c is the speed of light in a vacuum

f is the frequency of the wave

is the wavelength of the wave

For the blue light in this problem, we have

(frequency)

while the speed of light is

So, the wavelength of blue light is:

9)

The sound wave in this problem travels with uniform motion (=constant velocity), therefore we can use the following equation:

where

d is the distance covered by the wave

v is the speed of the wave

t is the time elapsed

In this problem:

v = 343 m/s is the speed of the sound wave

t = 0.287 s is the time elapsed

So, the distance covered by the wave is

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