Question

A bus moving with the speed \[10\,m{s^{ - 1}}\] on a straight road. A scooter wished to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

Answer 1

Hint: Use the relationship between distance, velocity and time to determine the velocity of the scooterist. When the two bodies move in the same direction, the relative velocity is the difference in the velocities of the two bodies.
\[v = \dfrac{d}{t}\]
Here, t is the time, d is the distance and v is the velocity.

Complete step by step answer:
Suppose, the velocity of the bus is \[{v_b}\] and the velocity of the scooterist is \[{v_s}\]. The velocity of the bus is given and it is \[10\,m{s^{ - 1}}\].

Since the bus and the scooterist move in the same direction, the relative velocity of the scooterist with respect to the bus is,
\[{v_{sb}} = {v_s} - {v_b}\]

Therefore, the relative velocity of the scooterist is,
\[{v_{sb}} = {v_s} - 10\]

We know that the relationship between velocity, distance and time is,
\[v = \dfrac{d}{t}\]

Here, t is the time, d is the distance and v is the velocity.

The relative velocity of the scooterist with respect to the bus is,
\[{v_{sb}} = \dfrac{d}{t}\]

Substitute \[{v_s} - 10\] for \[{v_{sb}}\], 1 km for d and 100 s for t in the above equation.
 \[{v_s} - 10 = \dfrac{{\left( {1\,km} \right)\left( {\dfrac{{1000\,m}}{{1\,km}}} \right)}}{{100\,s}}\]
\[ \Rightarrow {v_s} - 10 = 10\]
\[\therefore {v_s} = 20\,m{s^{ - 1}}\]

Therefore, the scooterist should chase the bus with velocity \[20\,m{s^{ - 1}}\].

Note:
When the two objects 1 and object 2 move in the same direction, the relative velocity of object 1 with respect to object 2 is different in the velocity of object 1 and velocity of object 2.