Compound Interest
October 20, 2022
Boast and Streams
October 24, 2022Â About this post
An important topic with application in problems on trains, boats and streams, circular motion etc. The entire topic revolves around one formula which is based on the relation between time, speed and distance.
The first section in this topic is an introduction where we look at the formula that explains the relation between time, speed and distance. We will also look at the various proportionals that can be derived from the formula. The exercises contain solved question and answers on time, speed and distance. When solving exercises, we recommend you to try solving the problems orally and with out using equations.
Introduction to Time, Speed and Distance
Relation Between Time, Speed and Distance
Speed = $\frac{\text{Distance Travelled}}{\text{Time Taken}}$
Unit Conversion
- To convert speed in km/hr to m/sec, multiply it with $\frac{5}{18}$
- To convert speed in m/sec to km/hr, multiply it with $\frac{18}{5}$
Identifying Proportionals
If A and B are two objects travelling at a speed
- Distance is constant:
   Speed is inversely proportional to Time. i.e if speed increases time taken to cover the same distance decreases.
Hence, if the ratio of speeds of A and B is s1 : s2, then the time taken by A and B to cover the same distance is in the ratio s2 : s1.
- Time is constant:
   Speed is directly proportional to the distance travelled.
Hence, Â if two objects A and B travel a distance of D1 and D2 with speeds S1 and S2 respectively, then
$\frac{S1}{S2} = Â \frac{D1}{D2}$
- Speed is constant:
   Distance travelled is directly proportional to the time taken.
Hence, if the time taken by A and B to cover a distance of D1 and D2 is T1 and T2 respectively, then
$\frac{T1}{T2} = Â \frac{D1}{D2}$
Average Speed
Average speed given by Total Distance travelled by Total time taken.
- If a man covers certain distance at u km/hr and an equal distance at v km/hr, then the average speed during the whole journey is given by
$\frac{2uv}{u+v}$ km/hr
- If a person travels for half the time at a speed of u km/hr and remaining half the time at v km/hr, then the average speed is given by
$\frac{u + v}{2}$ km/hr
