Distance = Speed$$\times$$Time
Speed = $$\frac{Distance}{Time}$$
Time = $$\frac{Distance}{Speed}$$
This is one of the most fundamental formulas and is used extensively throughout the topic.
Speed - Distance - Time
Very Important
Question 1
After any given time, the speed of a bus is directly proportional to the time elapsed since start. If it takes 4 hours to travel 100 km, how much distance will it travel in 6 hours?
Solution
Speed(S) $$\alpha\ $$ Time(T)
Therefore, S = kT
Distance(D) = Area of shaded region
= $$\frac{1}{2}\left(kT\right)\left(T\right)$$
= $$\frac{1}{2}kT^2$$
It is given,
100 = $$\frac{1}{2}k\left(4\right)^2$$
k = $$\frac{25}{2}$$
Distance travelled in 6 hours = $$\frac{1}{2}\left(\frac{25}{2}\right)\left(6\right)^2$$ = 225 km
Answer is option B.
Question 2
The length of a train is 440 metres. How much time does it take to cross a platform 1000 metres long if it is travelling at 72 kmph ?
Solution
Speed in m/s = 72/3.6 m/s = 20m/s Total distance = 1440 metres Total time taken = 1440/20 = 72 seconds.
Question 3
Ajay and Vijay race 2400 metres around a 400m circular track. Ajay is 50% faster than Vijay and gains a lap over him in 4 minutes. Find the time taken by Ajay to finish the race?
Solution
Let A be the speed of Ajay and V the speed of Vijay.
So, A = 150%V.
So, the relative speed of Ajay with respect to Vijay is V/2.
Time taken to run 400m at V/2 = 4 minutes.
Hence, $$V=\frac{2 * 400}{(4 * 60)} = \frac{10}{3}$$ m/s.
Therefore A=5 m/s.
So, time taken by Ajay to run 2400m is $$\frac{2400}{5} = 480s = 8$$ mins.
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Previous Year Stats
Speed - Distance - Time
19
questions from CAT exam over the past 5 years
Formulas Asked Together in Previous Papers
Relative Velocity
4 PYQsLinear Tracks
3 PYQsm/s to km/hr conversion.
2 PYQsBoats and Streams
2 PYQsCircular Tracks
1 PYQEscalators
1 PYQAverage Speed
1 PYQTrains
1 PYQ
