Motion Problems — From the Basics

Motion Problems — From the Basics. Practice questions to deepen understanding of motion problems from the basics. Online math practice with full solutions and step-by-step explanations.

Motion problems practice — 40 questions: speed/distance/time, meeting, chase, average speed, river and wind problems. Formulas and applications.

Part A: Foundational concepts (questions 1–10)

1. What speed is. 2–4. The three formulas (speed, distance, time). 5–7. Computing the basics.

40 questions

Question 1
2.50 pts

🚗 Basic concept:
What is speed?

Explanation:

💡 Detailed explanation:

Speed — how fast? 🏃

Real-life example:

🚗 A car travels at 60 km/h

What does that mean?
In every one hour it covers 60 km

Speed = distance ÷ time

If you traveled 120 km in 2 hours:
speed = 120 ÷ 2 = 60 km/h

Common units:
• km/h (kilometers per hour)
• m/s (meters per second)
• mph (miles per hour)

Correct answer: The distance a body travels per unit of time

Question 2
2.50 pts

🚗 :
velocity/speed?

Explanation:

💡 :

📐

distance-velocity/speed-

Question 3
2.50 pts

🚗 :
distance?

Explanation:

Explanation: See the relevant definition and formula above.

Question 4
2.50 pts

🚗 :
?

Explanation:

Explanation: See the relevant definition and formula above.

Question 5
2.50 pts

🚗 Basic exercise:
A car traveled 120 km in 2 hours.

What is the speed?

Explanation:

💡 Detailed explanation:

Simple computation 📝

Data:
distance = 120 km
time = 2 hours

Formula:
speed = distance ÷ time

Computation:
speed = 120 ÷ 2 = 60 km/h

Logic:
If in 2 hours it traveled 120 km,
in one hour it traveled half: 60 km

Correct answer: 60 km/h

Question 6
2.50 pts

🚗 Basic exercise:
A train travels at 90 km/h for 4 hours.

What distance did it cover?

Explanation:

💡 Detailed explanation:

Computing distance 📝

Data:
speed = 90 km/h
time = 4 hours

Formula:
distance = speed × time

Computation:
distance = 90 × 4 = 360 km

Logic:
90 km in each hour
In 4 hours: 90+90+90+90 = 360

Correct answer: 360 km

Question 7
2.50 pts

🚗 Basic exercise:
A motorcycle travels at 80 km/h.
The distance is 240 km.

How long will the trip take?

Explanation:

💡 Detailed explanation:

Computing time 📝

Data:
speed = 80 km/h
distance = 240 km

Formula:
time = distance ÷ speed

Computation:
time = 240 ÷ 80 = 3 hours

Verification:
80 km/h × 3 hours = 240 km ✓

Correct answer: 3 hours

Question 8
2.50 pts

⏱️ Unit conversion:
30 minutes equals how many hours?

Explanation:

💡 Detailed explanation:

Time conversion 📝

⭐ Important rule:

1 hour = 60 minutes

To convert minutes to hours:
Divide by 60

Computation:
30 minutes = 30 ÷ 60 = 0.5 hour

Conversion table:
15 minutes = 0.25 hour (quarter)
30 minutes = 0.5 hour (half)
45 minutes = 0.75 hour (three-quarters)
60 minutes = 1 hour

Correct answer: 0.5 hour (half an hour)

Question 9
2.50 pts

⏱️ Unit conversion:
1 hour and 15 minutes equals how many hours (in decimal)?

Explanation:

💡 Detailed explanation:

Combined conversion 📝

1 hour and 15 minutes:

1 hour = 1
15 minutes = 15 ÷ 60 = 0.25

Total:
1 + 0.25 = 1.25 hours

⚠️ Common mistake:
Writing 1.15 (wrong!)
15 minutes ≠ 0.15 hour

Rule: minutes ÷ 60, not ÷ 100!

Correct answer: 1.25 hours

Question 10
2.50 pts

⏱️ Unit conversion:
A speed of 72 km/h equals how many m/s (meters per second)?

Explanation:

💡 Detailed explanation:

Speed conversion 📝

⭐ Conversion rule:

km/h → m/s: divide by 3.6
m/s → km/h: multiply by 3.6

Why 3.6?
1 km = 1000 meters
1 hour = 3600 seconds
1000 ÷ 3600 = 1/3.6

Computation:
72 km/h = 72 ÷ 3.6 = 20 m/s

Verification: 20 × 3.6 = 72 ✓

Correct answer: 20 m/s

Question 11
2.50 pts

🚗 Exercise:
A cyclist traveled 15 km in 30 minutes.

What is the speed in km/h?

Explanation:

💡 Detailed explanation:

Solution steps 📝

Step 1: convert minutes to hours

30 minutes = 30 ÷ 60 = 0.5 hour

Step 2: compute speed

speed = distance ÷ time
speed = 15 ÷ 0.5 = 30 km/h

Logic:
If in half an hour it traveled 15 km,
in a full hour it travels double: 30 km

Correct answer: 30 km/h

Question 12
2.50 pts

🚗 Exercise:
A car travels at 60 km/h.
The distance is 20 km.

How many minutes will the trip take?

Explanation:

💡 Detailed explanation:

Computing time in minutes 📝

Step 1: compute time in hours

time = distance ÷ speed
time = 20 ÷ 60 = 1/3 hour

Step 2: convert to minutes

1/3 hour = (1/3) × 60 = 20 minutes

Logic:
60 km/h = 1 km per minute
So 20 km = 20 minutes

Correct answer: 20 minutes

Question 13
2.50 pts

🚗 :
-8:00 -10:00.
distance 100 .

velocity/speed ?

Explanation:

💡 :

velocity/speed 📝

1: calculate

-8:00 10:00 = 2

2: calculate velocity/speed

velocity/speed = distance ÷
velocity/speed = 100 ÷ 2 = 50

⭐ velocity/speed :
d
Question 14
2.50 pts

🚗 :
-14:00 180
velocity/speed 60 .

?

Explanation:

💡 :

📝

1: calculate

= distance ÷ velocity/speed
= 180 ÷ 60 = 3

2:

: 14:00
+ : 3

: 17:00

: 17:00

Question 15
2.50 pts

🚗 :
-9:00.
distance 45 velocity/speed 90 .

?

Explanation:

💡 :

📝

1: calculate

= distance ÷ velocity/speed
= 45 ÷ 90 = 0.5 = 30

2:

: 9:00
- : 30

: 8:30

: 8:30

Question 16
2.50 pts

🚗 Exercise:
A distance of 120 km.
Car A travels at 60 km/h.
Car B travels at 80 km/h.

How much earlier does car B arrive than car A?

Explanation:

💡 Detailed explanation:

Comparing times 📝

Time of car A:
120 ÷ 60 = 2 hours

Time of car B:
120 ÷ 80 = 1.5 hours

The difference:
2 - 1.5 = 0.5 hour = 30 minutes

Conclusion:
Car B (the faster one) arrives
30 minutes before car A

Correct answer: 30 minutes

Question 17
2.50 pts

🚗 Exercise:
The distance from home to work is 25 km.

What is the total distance Danny travels each day (round trip)?

Explanation:

💡 Detailed explanation:

Round trip = double! 📝

Distance in one direction: 25 km

Round trip:
There: 25 km
Back: 25 km

Total:
25 + 25 = 50 km

Or: 25 × 2 = 50 km

Correct answer: 50 km

Question 18
2.50 pts

🚗 Exercise:
A trip of 200 km at a speed of 100 km/h.
In the middle, a 30-minute stop.

What is the total time?

Explanation:

💡 Detailed explanation:

Travel time + stops 📝

Step 1: travel time only

time = 200 ÷ 100 = 2 hours

Step 2: add stop time

Stop: 30 minutes = 0.5 hour

Total time:
2 + 0.5 = 2.5 hours

⭐ Remember:
Total time = travel + stops

Correct answer: 2.5 hours

Question 19
2.50 pts

🚗🚙 :
.
distance ?

Explanation:

💡 :

📝

- !
Question 20
2.50 pts

🚗🚙 Meeting problem:
Two cars set out at the same time toward each other.
The distance between them is 200 km.
Speeds: 60 km/h and 40 km/h.

After how much time will they meet?

Explanation:

💡 Detailed explanation:

Closing speed method 📝

Step 1: compute closing speed

Traveling toward each other →
closing speed = 60 + 40 = 100 km/h

Step 2: compute time to meeting

time = distance ÷ closing speed
time = 200 ÷ 100 = 2 hours

Verification:
Car 1 traveled: 60×2 = 120 km
Car 2 traveled: 40×2 = 80 km
Total: 120+80 = 200 km ✓

Correct answer: 2 hours

Question 21
2.50 pts

🚗🚙 Meeting problem:
A car leaves city A toward city B (100 km away) at 50 km/h.
A car leaves city B toward city A at 50 km/h.
They depart at the same time.

At what distance from city A will they meet?

Explanation:

💡 Detailed explanation:

Equal speeds = meeting in the middle! 📝

Closing speed:
50 + 50 = 100 km/h

Time to meeting:
100 ÷ 100 = 1 hour

Distance the car from A traveled:
50 × 1 = 50 km

⭐ Rule:
When the speeds are equal,
the meeting point is at the midpoint of the route!

Correct answer: 50 km (in the middle)

Question 22
2.50 pts

🚗🚙 Meeting problem:
The distance between two cities is 180 km.
Car A leaves from the west at 80 km/h.
Car B leaves from the east at 40 km/h.
They depart at the same time.

At what distance from the western city will they meet?

Explanation:

💡 Detailed explanation:

Finding the meeting location 📝

Step 1: closing speed
80 + 40 = 120 km/h

Step 2: time to meeting
180 ÷ 120 = 1.5 hours

Step 3: distance traveled by car A
80 × 1.5 = 120 km

⭐ Rule:
The faster one travels more!
Car A (80 km/h) traveled twice as much as car B (40 km/h)

Correct answer: 120 km

Question 23
2.50 pts

🚗🚙 Meeting problem:
Car A leaves at 8:00 from point A toward B at 60 km/h.
Car B leaves at 9:00 from B toward A at 80 km/h.
The distance A-B is 200 km.

At what time will they meet?

Explanation:

💡 Detailed explanation:

Departures at different times 📝

Step 1: what happened by 9:00?

Car A traveled one hour:
60 × 1 = 60 km

Distance remaining: 200 - 60 = 140 km

Step 2: closing speed (from 9:00)
60 + 80 = 140 km/h

Step 3: time to meeting
140 ÷ 140 = 1 hour

Meeting time:
9:00 + 1 hour = 10:00

Correct answer: 10:00

Question 24
2.50 pts

🚗🚗 :
because.
, .

velocity/speed ?

Explanation:

💡 :

because 📝

because
Question 25
2.50 pts

🚗🚗 :
-60 .
30 -90 .

( ) ?

Explanation:

💡 :

📝

1:

1 30 = 0.5
distance: 60 × 0.5 = 30

2: velocity/speed

because → :
90 - 60 = 30

3:

30 ÷ 30 = 1
<
Question 26
2.50 pts

🚗🚗 Separation problem:
Two cars leave from the same point in opposite directions.
Speeds: 70 km/h and 50 km/h.

What is the distance between them after two hours?

Explanation:

💡 Detailed explanation:

Separation = sum! 📝

Opposite directions → separating!

Separation speed:
70 + 50 = 120 km/h

Distance after two hours:
120 × 2 = 240 km

Or separately:
Car 1: 70 × 2 = 140 km
Car 2: 50 × 2 = 100 km
Total: 140 + 100 = 240 km

Correct answer: 240 km

Question 27
2.50 pts

🚗 Concept:
What is the correct formula for average speed?

Explanation:

💡 Detailed explanation:

⚠️ Common mistake! 📝

❌ Common mistake:

Computing the mean of the speeds:
(60 + 40) ÷ 2 = 50 km/h

✅ The correct formula:

average speed = total distance ÷ total time

Why?
Because we do not always travel the same time at each speed!

Correct answer: average speed = total distance ÷ total time

Question 28
2.50 pts

🚗 Exercise:
I traveled 60 km at 60 km/h,
and then another 60 km at 30 km/h.

What is the average speed?

Explanation:

💡 Detailed explanation:

Correct computation of average speed 📝

Step 1: compute times

Segment 1: 60 ÷ 60 = 1 hour
Segment 2: 60 ÷ 30 = 2 hours

Step 2: sum

Total distance: 60 + 60 = 120 km
Total time: 1 + 2 = 3 hours

Step 3: average speed

120 ÷ 3 = 40 km/h

⚠️ Note: Not 45! (not the mean of 60 and 30)

Correct answer: 40 km/h

Question 29
2.50 pts

🚗 Exercise:
I drove to work (30 km) at 60 km/h.
I drove back along the same route at 30 km/h.

What is the average speed for the entire trip?

Explanation:

💡 Detailed explanation:

Round trip 📝

Outbound:
distance: 30 km
time: 30 ÷ 60 = 0.5 hour

Return:
distance: 30 km
time: 30 ÷ 30 = 1 hour

Total:
distance: 30 + 30 = 60 km
time: 0.5 + 1 = 1.5 hours

Average speed:
60 ÷ 1.5 = 40 km/h

Correct answer: 40 km/h

Question 30
2.50 pts

🚗 Shortcut formula:
For a round trip over the same distance,
where outbound speed is v₁ and return speed is v₂,

what is the shortcut formula for the average speed?

Explanation:

💡 Detailed explanation:

Special formula for a round trip! 📝

⭐ The formula:

average = 2v₁v₂ / (v₁ + v₂)

This is called the "harmonic mean"

Example:
v₁ = 60, v₂ = 30

average = (2 × 60 × 30) / (60 + 30)
= 3600 / 90
= 40 km/h

Why not 45?
Because we spent more time at the slower speed!

Correct answer: 2v₁v₂ / (v₁ + v₂) — harmonic mean

Question 31
2.50 pts

🚗 :
-80 60 ,
30 .

distance?

Explanation:

Explanation: See the relevant definition and formula above.

Question 32
2.50 pts

🚃🚶 :
4 -5 .
-20 .

velocity/speed ?

Explanation:

💡 :

distance, 📝

Question 33
2.50 pts

🚤 Problem:
A boat travels downstream (with the current) at 20 km/h
and upstream (against the current) at 12 km/h.

What is the boat's speed in still water?

Explanation:

💡 Detailed explanation:

River and current problems 📝

1: calculate distance

: 5 × 4 = 20

2:

20 = 20/60 = 1/3

3: velocity/speed

velocity/speed = distance ÷
= 20 ÷ (1/3)
= 20 × 3
= 60
⭐ Principle:

Downstream: boat speed + current
Upstream: boat speed - current

Let:
s = boat speed
c = current speed

Equations:
s + c = 20
s - c = 12

Add:
2s = 32
s = 16 km/h

(and current speed: c = 4 km/h)

Correct answer: 16 km/h

Question 34
2.50 pts

✈️ Problem:
A plane flies with the wind at 600 km/h
and against the wind at 500 km/h.

What is the wind speed?

Explanation:

💡 Detailed explanation:

Wind problems 📝

Let:
p = plane speed
w = wind speed

Equations:
p + w = 600 (with the wind)
p - w = 500 (against the wind)

Subtract:
(p+w) - (p-w) = 600 - 500
2w = 100
w = 50 km/h

(plane speed: p = 550 km/h)

Correct answer: 50 km/h

Question 35
2.50 pts

🚃🚃 :
200 -72 .
300 -54 .
( because)

?

Explanation:

Explanation: See the relevant definition and formula above.

Question 36
2.50 pts

🚃🌉 Problem:
A train of length 100 m travels at 36 km/h.
It crosses a bridge of length 400 m.

How long is the train on the bridge (any part of it)?

Explanation:

💡 Detailed explanation:

Train on a bridge 📝

⭐ Total distance:

From the moment the front of the train enters the bridge
until the rear of the train exits the bridge:

bridge length + train length
400 + 100 = 500 m

Speed in m/s:
36 ÷ 3.6 = 10 m/s

Time:
500 ÷ 10 = 50 seconds

Correct answer: 50 seconds

Question 37
2.50 pts

🚗 Problem:
A trip of 300 km.
First half at 100 km/h, a 1-hour stop, second half at 75 km/h.

What is the total time?

Explanation:

💡 Detailed explanation:

Trip with a break 📝

First half:
distance: 150 km
time: 150 ÷ 100 = 1.5 hours

Stop: 1 hour

Second half:
distance: 150 km
time: 150 ÷ 75 = 2 hours

Total:
1.5 + 1 + 2 = 4.5 hours

Correct answer: 4.5 hours

Question 38
2.50 pts

🚌 :
6 .
velocity/speed 50 .

-5 ?

Explanation:

💡 :

📝

distance :
50 × 6 = 300

-5 :
300 × 5 = 1,500

: 1,500

Question 39
2.50 pts

⚠️ :
?

Explanation:

💡 :

! ⚠️

Question 40
2.50 pts

📋 :
?

Explanation:

💡 :

! 📋

-