Distance
Define "distance" in your own words.
distance is the total length of the path traveled
How does displacement differ from distance?
Unlike distance, it is concerned with straight-line change, not path length
Define "velocity" and explain how it's different from speed.
Velocity is speed with direction
Define "acceleration".
Acceleration is the rate of change of velocity
State the numerical value of the acceleration due to gravity near Earth's surface that you should use for a problem in meters.
9.81 m/s2
Identify the type of quantity for the unit:
meter (m)
distance
A runner completes a lap around a 400 m track. What is the runner's distance traveled after one lap?
400 m
A walker goes 200 m north then 150 m north. What is the displacement? Include direction.
200+150=350 m north
A car travels 1500 m east in 30 s. Calculate the car's average speed.
(1500 m)/(30 s)
=50 m/s
A car's velocity changes from 10 m/s to 20 m/s in 5.0 s. Calculate the average acceleration. Include units.
a=
(20−10)/5
=2.0 m/s2.
An object is dropped from rest. After 2.0 s, what is its speed, neglecting air resistance? Use 9.81 m/s2 and include units.
19.62 m/s
Identify the type of quantity for the unit:
nanoseconds
time
A car drives 120 m east, then 80 m west. What is the total distance traveled?
120+80=200 m
A student walks 50 m west, 120 m east, then 30 m west. What is their net displacement?
West 50 = −50
East 120 = +120
West 30 = −30
→ net = 40 m east.
A cyclist covers 9.0 km north in 30 minutes. Calculate the average speed in m/s.
**Hint: change km to meters and minutes to seconds**
9.0 km=9000 m, 30 min=1800 s
9000/1800
=5.0 m/s
A skateboarder slows from 8.0 m/s to 2.0 m/s in 3.0 s. What is the acceleration? Include units and determine if the acceleration is positive or negative.
a=
(2.0-8.0)/3.0
= -2.0 m/s^2
A ball is dropped from a height and hits the ground after 3.0 s. Calculate the height it was dropped from. Use 9.81 m/s2 and include units.
d =
(9.81*3.0^2)/2
= 44.1 meters
Identify the type of quantity for the unit:
m/s2
Acceleration
A bicyclist rides 3.2 km to a park, then rides another 4.5 km exploring, then returns straight home 5.0 km. What is the total distance traveled in meters?
3.2+4.5+5.0=12.7 km=12,700 m
A hiker starts at point A, goes 2.0 km east, then 1.2 km north. What is the hiker’s displacement from point A? Include direction.
Magnitude =
sqrt((2.0)^2+(1.2)^2)=
sqrt5.44
≈ 2.33 km NE
A jogger runs east 400 m in 2.0 min, then rests 30 s, then runs west 100 m in 40 s. Calculate the jogger's average velocity for the entire activity (include direction).
Net displacement = 400−100=300 m east.
Total time = 2.0 min=120 s+30 s+40 s=190 s
Average velocity =
(300 m)/(190 s)
≈58 m/s east
Given initial velocity is at rest and final velocity is 15.0 m/s over a time interval of 4.0 s, calculate the acceleration and interpret the sign. Include units.
a=
(15.0-0)/4.0
=3.75 m/s^2
A rock is dropped from a cliff and hits the ground at a velocity of 124 ft/s. How long was it in free fall? Use 32.2 ft/s2 and include units.
t =
(124 (ft)/s)/(32.2 (ft)/s^2)
3.85 seconds
Identify the type of quantity for the unit:
km/year
A delivery driver makes stops along a route with segments of 2.4 km, 1.75 km, 3.05 km, and 0.9 km. They start at the depot and finish at the last stop (no return to depot). Compute the total distance traveled in meters.
Total = 2.4+1.75+3.05+0.9=8.10 km= 8,100 m
A boat sails from the dock 3.0 km west and then 4.0 km north. How far is the boat from the dock in a straight line, and in what general direction is it from the dock?
Distance =
sqrt(3.0^2+4.0^2)
=5.0 km NW
A delivery van drives at a constant velocity of12.5 m/s east. How long (in seconds) will it take the van to travel 3.75 km?
**Hint: change km to meters**
3.75 km=3750 m
Time =
(3750 m)/(12.5 m/s)
=300 s
A train speeds up uniformly from 20 km/hr at a rate of 10 km/hr2 for 0.5 hours. How fast is the train moving after 15 seconds?
a = 10 km/hr2 and t = 0.5 hours
change in velocity =
10*0.5 = 5 km/hr
final velocity = initial velocity + change in velocity
= 20 + 5 = 25 km/hr
A skydiver jumps from a plane at an altitude of 5,000 feet. How long will his jump last? Use 32.2 ft/s and include units.
5000=(32.2*t^2)/2
10000=32.2*t^2
310.56=t^2
sqrt(310.56)=t
17.6 seconds
Identify the type of quantity for the unit:
650 km NW
displacement