Scalar & Vector
Which of the following quantities is a scalar?
A. Velocity
B. Displacement
C. Speed
D. Force
C. Speed
What is the main difference between speed and velocity?
Speed only tells how fast an object moves.
Velocity tells how fast and in which direction the object moves.
What is the main difference between distance and displacement?
Distance is the total path traveled.
Displacement is the straight-line change from start to end with direction.
What does the slope of a speed–time graph represent?
Acceleration.
Can a distance–time graph ever go downward? Explain.
No. Because distance is the total path traveled and cannot decrease.
Which list contains only vectors?
A. Speed, distance, time
B. Velocity, force, acceleration
C. Distance, speed, mass
D. Energy, time, temperature
B. Velocity, force, acceleration
A car travels 60 km north in 1 hour.
a) What is the average speed?
b) What is the average velocity?
Average speed = 60 km/h
Average Velocity = 60 km/h north
Why can displacement be zero while distance is not zero?
Because the object may return to the starting point, so displacement is zero but distance is the total path traveled.
What does a horizontal line on a speed–time graph represent?
A. Acceleration
B. Constant speed
C. At rest
B. Constant speed
Which graph shows faster motion?
Graph A: steeper line
Graph B: less steep line
Answer:
Graph A
Because a steeper slope means a higher speed.
A student walks 5 m east and then 5 m west.
a) Total distance traveled:
b) Displacement:
a) Total distance traveled:
10 m
b) Displacement:
0 m
Can the student have speed but zero velocity? Why?
Yes. The student moved (so speed exists), but the starting point and ending point are the same, so displacement is zero, meaning velocity is zero.
A student walks 10 m east and then 5 m east.
a) What is the distance traveled?
b) What is the displacement?
a) What is the distance traveled?
Answer:
10 + 5 = 15 m
b) What is the displacement?
Answer:
15 m east
A bicycle moves at a constant speed of 6 m/s for 8 seconds.
Draw the speed–time graph.
Graph: horizontal line at 6 m/s
A student walks at a constant speed away from the starting point.
Draw the distance–time graph.
The graph should be:
A straight line
Increasing distance
Constant slope
A student walks 6 m east, then 8 m north.
a) Total distance traveled:
b) Magnitude of displacement:
a) Total distance traveled:
6 + 8 = 14 m
b) Magnitude of displacement:
10m
A cyclist travels 30 km east in 2 hours. What is the average speed in m/s?
4.17m/s
A person walks:
6 m east
8 m north
a) Total distance traveled =
b) Magnitude of displacement =
a) Total distance traveled =14m
b) Magnitude of displacement =10m
A car moves at 12 m/s and slows down to 0 m/s in 6 seconds.
a) Draw the graph.
b) Calculate decceleration.
Graph: straight line downward
-2m/s2
A car starts slow and moves faster and faster.
Draw the distance–time graph.
The graph is a curve upward.
Because:
speed increases
slope increases
Curve getting steeper over time.
A plane flies 300 km east and 400 km north.
a) Magnitude of displacement:
b) Is distance or displacement larger? Explain why.
a) Answer: 500 km
b) Distance is larger.
Distance = 300 + 400 = 700 km
Displacement = 500 km
This is because distance is the total path traveled, while displacement is the straight-line change from start to end.
A car drives around a circular track and returns to the starting point.
Distance traveled = 500 m
a) What is the displacement?
b) If the trip took 50 s, what is the average speed?
c) What is the average velocity?
0m
10m/s
0m/s
Can distance and displacement have the same value? Explain.
Answer:
Yes. When an object moves in a straight line without changing direction, distance equals displacement.
A car:
starts from rest
accelerates to 8 m/s in 4 s
then moves at constant speed for 6 s
1️⃣ 0–4 s
straight line up
2️⃣ 4–10 s
horizontal line
Draw a distance–time graph for this motion:
move at constant speed for 5 s
stop for 2 s
move faster for 3 s
Graph segments:
1️⃣ 0–5 s
straight line
2️⃣ 5–7 s
horizontal line
3️⃣ 7–10 s
steeper straight line