Answer to Question #334774 in Math for Agl

Question

3. Mrs. Mariann Alvarez is approaching a stoplight moving with a

velocity of +25.0 m/s. The light turns yellow, and Ima applies the

brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then

determine the displacement of the car during the skidding process.

(Note that the direction of the velocity and the acceleration vectors

are denoted by a + and a - sign.) (3 points)

4. Riza is waiting at a stoplight. When it finally turns green, Riza

accelerated from rest at a rate of a 4.75.00 m/s2 for a time of 4.30

seconds. Determine the displacement of Riza's car during this time

period. (3 points)

Answer 1

3.

$$s=v_0t+\dfrac{at^2}{2}$$

$$v=v_0+at=0=>t=-\dfrac{v_0}{a}$$

Then

$$s=v_0(-\dfrac{v_0}{a})+\dfrac{a(-\dfrac{v_0}{a})^2}{2} =-\dfrac{v_0^2}{2a}$$

$$s=-\dfrac{(25m/s)^2}{2(-8m/s^2)}=39.0625m$$

4.

$$s=\dfrac{at^2}{2}=\dfrac{4.75m/s^2(4.3s)^2}{2}=43.91375m$$