Question

A passenger is at a distance of 10 m from a bus when the bus starts with a constant acceleration of $0.1m{s}^{-2}$. The velocity with which the passenger
should run towards the bus so as to catch the bus in $30sec$ is _________.

• A. 2.5 m s^–1
• B. 2 m s^–1
• C. 3.5 m s^–1
• D. 1.83 m s^–1

Answer 1

The correct option is D

1.83 m s^–1

Step 1 Assigning variables

let x= Distance covered by bus , a= acceleration , t = time

Initial speed of the bus, u = 0

v= velocity of person

Step 2 Calculation

Using equation of motion

$$\begin{gathered} x=\frac{1}{2}a{t}^2 \\ x=\frac{1}{2}0.1{\left(30\right)}^2 \end{gathered}$$

Equating distances

$x+10=vt$

$$\begin{gathered} \frac{1}{2}(0.1){\left(30\right)}^2+10=v\left(30\right) \\ 55=v\left(30\right) \\ v=1.83m{s}^{-1} \end{gathered}$$

Answer Option D is correct.