Question

The brake applied to an car reduce the acceleration 6 m/s in the opposite direction to the motion.if the car takes two seconds to stop after the application of the brake.calculate the distance travelled by the car after applying brake

Answer 1

Let's first find the initial velocity of the car from the kinematic equation:

$$v_f = v_i + at,$$

here, $v_i$ is the initial velocity of the car, $v_f = 0$ is the final velocity of the car, $a = -6 m/s^2$ is the deceleration of the car and $t = 2 s$ is the time during which the car decelerates.

Then, from this formula we can calculate the initial velocity of the car:

$$v_i = -at =- (-6 \dfrac{m}{s^2}) \cdot 2.0 s = 12 \dfrac{m}{s}.$$

Finally, we can find the distance travelled by the car after applying brake from another kinematic equation:

$$d = v_it + \dfrac{1}{2}at^2 = 12 \dfrac{m}{s} \cdot 2.0 s + \dfrac{1}{2} \cdot (-6 \dfrac{m}{s^2}) \cdot (2.0 s)^2 = 12 m.$$

Answer:

$d =12 m.$