Question

A bus is moving with a velocity 10 m/s. A motor cyclist wishes to overtake the bus in 60 s. With what velocity the motor cyclist should chase the bus which is 1 km ahead of him?
(a) 28.67m/s (b) 26.67 m/s (c) 34.56 m/s (d)none​

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Velocity of the bus (V₁) = 10ms⁻¹.
• Time (t) = 60 seconds.
• Distance (s) = 1km ⇒ 1000 m.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

• Velocity the motorcyclist (V₂)

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

We can calculate the velocity of the motorcyclist:

$\mapsto \sf Velocity =\dfrac{Distance }{time}$

Substituting the values, we get:

$\sf \to V=\dfrac{1000}{60}$

$\to \sf V=\dfrac{50}{3} ms^{-1}$

Now, required velocity can be calculated as:

$\mapsto \sf{\green{V=V_2-V_1}}$

Substitute.

$\sf \to \dfrac{50}{3}=V_2 - 10$

$\sf \to V_{2}=\dfrac{50}{3}+10$

$\to \sf V_2=\dfrac{80}{3}$

$\leadsto \sf{\red{ V_2=26.67 ms^{-1}}}$

The cyclist should go at the speed of 26.67 ms⁻¹.

OPTION (b) IS CORRECT!