Shortcut– Time, Speed and Distance
Relative Speed – Same direction:
When two objects are moving we have to take relative speed for the
calculation.
Relative speed of two objects moving in same direction
= S1 - S2
Relative speed of two objects moving in opposite direction
= S1 + S2
Question:
A thief standing 50 away from a dog starts running away from it at a speed of 2 m/s. The dog suddenly starts chasing him at a speed of 3m/s. How long will the dog take to catch the thief?
Answer:D = 50m;
S1 = 3;
S2 = 2
Time taken, T = 50/(3-2) = 50 seconds
Distance travelled by the thief = Speed x Time to catch
= 2 x 50 = 100 m
Shortcut– Time, Speed and Distance
Relative Speed – Opposite direction:
When two objects are moving we have to take relative speed for the
calculation.
Relative speed of two objects moving in same direction
= S1 - S2
Relative speed of two objects moving in opposite direction
= S1 + S2
Time taken=Distance/Relative speed
Question:
Two friends start from their home 300 m apart and walk towards each other at a speed of 2mps and 3mps. How long (in minutes) will they take to meet each other?
Answer:
D = 300m
S1 = 2mps;
S2 = 3mps
T = 3000/(2+3) = 60 seconds
Time taken in minutes = 60/60 = 1 minute.
Shortcut– Time, Speed and Distance
Average Speed – Different distance and time
Question:
A man travels from a point to other. The first 100 km he travels at a speed of 25 kmph. The next 80 km he travels at a speed of 40 kmph. The last 120 km he travels at a speed of 20 kmph. What is the average speed of his journey?
Answer:
=$\dfrac{100+80+120}{\dfrac{100}{25}+\dfrac{80}{40}+\dfrac{120}{20}}$
= 300/12
= 25 kmph
Shortcut– Time, Speed and Distance
Average Speed – Distance is same. General formula when distance is same in all the cases.
Question:
Sai travels from her house to office at a speed of 50kmph. She suddenly returns home at a speed of 60kmph. What is her average speed?
Answer:
$S_{1}$ = 50;
$ S_{2}$ = 60
$S_{a}$ = 2(50x60)/(50+60)
= 6000/110
= 54.54 kmph
Note: Distance value is unnecessary.
Shortcut– Time, Speed and Distance
Average Speed – Time taken is same in all the cases.
Average speed=$\dfrac{S_{1}+S_{2}+S_{3}}{3}$
Question:
A man travels from a point to other. The first 100 km he travels at a speed of 50 kmph. The next 80 km he travels at a speed of 40 kmph. The last 120 km he travels at a speed of 60 kmph. What is the average speed of his journey?
Answer:
Time taken in the first case = 100/50 = 2 hours
Time taken in the second case = 80/40 = 2 hours
Time taken in the third case = 120/60 = 2 hours
Time taken is same in all the cases. So, average speed can be calculated by
directly taking the average of the speeds in each case.
Average speed = (50 + 40 + 60)/3
= 50 kmph
Shortcut– Time, Speed and Distance
Circular race – Time in which the runners meet at the starting point
D – Circumference of the race track.
S1, S2, … , Sn – Speed of the individual runners.
T1, T2 , … , Tn – Time taken by the respective runners to complete one round
the track.
Question:
Three persons participate in a race on a circular track of length 400m. They can run at a speed of 2mps, 4mps and 5mps respectively. How long will they take to meet in the starting point for the first time?
Answer:Time taken by each person to complete one circle
Person 1 = 400/2 = 200 seconds = $T_{1}$
Person 2 = 400/4 = 100 seconds =$ T_{2}$
Person 3 = 400/5 = 80 seconds = $T_{3}$
LCM($T_{1}, T_{2}, T_{3}$) = 400 seconds
Time taken by them to meet at starting point for the first time = 400 seconds.