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# 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/sB. 20 m/sC. 50 m/sD 30 m/s

Last updated date: 12th Sep 2024
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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
\$
\because s = \dfrac{{{d_1}}}{t} \\
\therefore {d_1} = s*t \\
{d_1} = 10*100 = 1000m \\
\$
Now we will find distance travelled by scooterist to overtake bus i.e.
\$
d = {d_1} + 1000 \\
d = 1000 + 1000 \\
d = 2000m \\
\$
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 = \dfrac{d}{t} = \dfrac{{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}}\$