Question

A scooterist sees a bus 1 km ahead of him moving with a velocity of 10 m/s. With what speed the scooterist should move so as to overtake the bus in 100 s.
A. 10 m/s
B. 20 m/s
C. 50 m/s
D 30 m/s

Answer 1

Hint Since we know speed is to distance divided by time taken. We will use the relation to find the answer. Distance travelled by scooterists to overtake a bus is 1 km plus distance moved by bus in 100 s.

Step by step solution
According the question
Firstly, we will find the distance travelled by bus in 100 sec i.e. $d_1$
Let s be the speed of bus, given by
$$\begin{gathered} \because s={\displaystyle \frac{d_1}{t}} \\ \therefore d_1=s\ast t \\ {d}_1=10\ast 100=1000m \end{gathered}$$
Now we will find distance travelled by scooterist to overtake bus i.e.
$$\begin{gathered} d=d_1+1000 \\ d=1000+1000 \\ d=2000m \end{gathered}$$
Let S be the required speed to overtake the bus in 100 sec
Hence to overtake bus in 100 sec speed of scooterist should be
$S={\displaystyle \frac{d}{t}}={\displaystyle \frac{2000}{100}}=20m{s}^{-1}$

Hence option B is correct.

Note We can also solve this problem using the concept of relative velocity.
Given, t = 100s,
s = 1000m;
v = 10m/s.
But this is the relative speed with respect to the bus

$V_s$ = actual velocity of scooter;
$V_b$ = velocity of bus;
$v$ = relative velocity of scooter with respect to bus.

$v=V_s-V_b$ as both bus and scooter are moving in same direction

$$\therefore 10=V_s-10$$
Hence, $V_b=20m{s}^{-1}$

But this is the relative speed with respect to the bus

$V_s$ = actual velocity of scooter;
$V_b$ = velocity of bus;
$v$ = relative velocity of scooter with respect to bus.

$v=V_s-V_b$ as both bus and scooter are moving in same direction

$$\therefore 10=V_s-10$$
Hence, $V_b=20m{s}^{-1}$