Question

A car is traveling at a constant velocity of 30 m/s when the driver suddenly applies the brakes, causing the car to decelerate at a constant rate of -5 m/s^2. Assume the initial position of the car is 0 m.

a) Determine the time it takes for the car to come to a complete stop.

b) Calculate the distance traveled by the car during the deceleration.

Answer

a) To determine the time it takes for the car to come to a complete stop, we can use the** equation of motion**:

where:
$v$ is the final velocity (0 m/s, since the car comes to a stop),
$u$ is the initial velocity (30 m/s),
$a$ is the acceleration (-5 m/s^2),
and $t$ is the time we want to solve.

Rearranging the equation, we get:

Substituting the given values into the equation:

Therefore, it takes the car 6 seconds to come to a complete stop.

b) To calculate the distance traveled by the car during the deceleration, we can use the equation of motion:

where:
$s$ is the displacement or distance traveled,
$u$ is the initial velocity (30 m/s),
$a$ is the acceleration (-5 m/s^2),
and $t$ is the time taken (6 s in this case).

Substituting the given values into the equation:

Simplifying the equation:

Therefore, the car travels a distance of 90 meters during the deceleration.