1. Intro to Physics Units

The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds. What are the units of A and B?

Write the following numbers in powers of 10 notation: 0.219.

Write out the following numbers in full with the correct number of zeros: 2.5 x 10⁻¹

Time intervals measured with a physical stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of 4.5 min?

A watch manufacturer claims that its watches gain or lose no more than 9 seconds in a year. How accurate are these watches, expressed as a percentage?

Write the following as full (decimal) numbers without prefixes on the units: 22.5 nm.

Express the following using the prefixes of Table 1–4: 18 x 10² bucks.

The lowest and highest natural temperatures ever recorded on earth are −129°F in Antarctica and 134°F in Death Valley. What are these temperatures in °C and in K?

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in years.

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express using a metric prefix (km).

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for $0.150$ s. The first officer on the spacecraft measures that the searchlight is on for $12.0$ ms.

(a) Which of these two measured times is the proper time?

(b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light $c$?

The positive muon (µ⁺), an unstable particle, lives on average 2.20 × 10^-6 s (measured in its own frame of reference) before decaying. What average distance, measured in the laboratory, does the particle move before decaying?

A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light.

A proton has momentum with magnitude p₀ when its speed is 0.400c. In terms of p₀, what is the magnitude of the proton's momentum when its speed is doubled to 0.800c?

X rays with initial wavelength $0.0665$ nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?