Question

A car is moving along a straight road with a constant velocity of 20 m/s. The driver applies the brakes, and the car decelerates at a constant rate of \(4 \, \text{m/s}^2\). How much time will it take for the car to come to rest?

• A. \( 5 \, \text{seconds} \)
• B. \( 10 \, \text{seconds} \)
• C. \( 4 \, \text{seconds} \)
• D. \( 2 \, \text{seconds} \)

Hint:

When an object comes to rest, the final velocity is zero. Use the first equation of motion \( v = u + at \) to find the time taken for the object to stop.

Answer 1

The Correct Option is A

Step 1: Data Assimilation.

- Initial car velocity: \( u = 20 \, \text{m/s} \}
- Final car velocity: \( v = 0 \, \text{m/s} \) (car immobilized)
- Car deceleration: \( a = -4 \, \text{m/s}^2 \) (negative due to velocity reduction)

Step 2: Application of First Kinematic Equation.

The foundational kinematic equation links velocity, acceleration, and time:

\[
v = u + at
\]

Substitution of provided values:

\[
0 = 20 + (-4) \times t
\]

\[
-20 = -4t
\]

\[
t = \frac{-20}{-4} = 5 \, \text{seconds}
\]


Conclusion: The duration for the car to attain a standstill is \( 5 \, \text{seconds} \).