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: Understand the given data. - Initial velocity of the car, \( u = 20 \, \text{m/s} \) - Final velocity of the car, \( v = 0 \, \text{m/s} \) (since the car comes to rest) - Acceleration (deceleration), \( a = -4 \, \text{m/s}^2 \) (negative because the car is slowing down) Step 2: Use the first equation of motion. The first equation of motion relates velocity, acceleration, and time: \[ v = u + at \] Substitute the known values: \[ 0 = 20 + (-4) \times t \] \[ -20 = -4t \] \[ t = \frac{-20}{-4} = 5 \, \text{seconds} \] Answer: Therefore, the time taken for the car to come to rest is \( 5 \, \text{seconds} \).