Answer to Question #244646 in Physics for Have a good day

Question

You are driving your car, and the traffic light ahead turns red. You apply the brakes for 2.94 s, and the velocity of the car decreases to +5.35 m/s. The car’s deceleration has a magnitude of 2.98 m/s2 during this time. What is the car’s displacement?

Answer 1

Let's first find the initial velocity of the car:

$$v=v_0+at,$$ $$v_0=v-at=5.35\ \dfrac{m}{s}-(-2.98\ \dfrac{m}{s^2})\cdot2.94\ s=14.11\ \dfrac{m}{s}.$$

Finally, we can find the car’s displacement:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=14.11\ \dfrac{m}{s}\cdot2.94\ s+\dfrac{1}{2}\cdot(-2.98\ \dfrac{m}{s^2})\cdot(2.94\ s)^2=28.6\ m.$$