Question

A car is moving along a straight line and is brought to a stop within a distance of \(200\) m and in time \(10\) s. The initial speed of the car is

• A. \(25\ \text{m s}^{-1}\)
• B. \(50\ \text{m s}^{-1}\)
• C. \(75\ \text{m s}^{-1}\)
• D. \(40\ \text{m s}^{-1}\)

Hint:

When a body comes to rest under uniform deceleration, the average velocity is \[ \frac{u+v}{2}. \] Using \[ s=\frac{u+v}{2}\,t \] often provides the quickest solution.

Answer 1

The Correct Option is D

Step 1: Use kinematics — car decelerates uniformly to rest.
Given: distance \( s = 200\text{ m} \), time \( t = 10\text{ s} \), final velocity \( v = 0 \).

Step 2: Apply \( s = \frac{(u+v)}{2}\cdot t \).
\( 200 = \frac{u+0}{2}\times 10 \Rightarrow u = \frac{400}{10} = 40\text{ m/s} \)

\[ \boxed{u = 40\text{ m/s}} \]