Question

1. Renz is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Renz applies the brakes and skids to a stop. If Renz acceleration is -8.00 m/s², then determine the displacement of the car during the skidding process.

2. A car slows down its motion from 10 m/s to 6 m/s in 2 seconds under constant acceleration. What is its acceleration?

3. A car starts its motion from rest and uniformly accelerates at a rate of 4 m/s² for 2 seconds in a straight line. How far did the car travel during those 2 seconds?

4. An object, without change in direction, travels a distance of 50 m with an initial speed of 5 m/s in 4 s. Find the object's velocity at the end of the given time interval? 

5. Ben Simmons is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of 6.00 m/s² for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period.

 

 

 

 

 

 

 

 

 

 

Answer 1

1)

$$v^2=v_0^2+2ad,$$ $$0=v_0^2+2ad,$$ $$d=-\dfrac{v_0^2}{2a}=-\dfrac{(30\ \dfrac{m}{s})^2}{2\times(-8\ \dfrac{m}{s^2})}=56.25\ m.$$

2)

$$v=v_0+at,$$ $$a=\dfrac{v-v_0}{t}=\dfrac{6\ \dfrac{m}{s}-10\ \dfrac{m}{s}}{2\ s}=-2\ \dfrac{m}{s}.$$

3)

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=0+\dfrac{1}{2}\times4\ \dfrac{m}{s^2}\times(2\ s)^2=8\ m.$$

4)

$$d=\dfrac{1}{2}(v_0+v)t,$$ $$v=\dfrac{2d}{t}-v_0=\dfrac{2\times50\ m}{4\ s}-5\ \dfrac{m}{s}=20\ \dfrac{m}{s}.$$

5)

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=0+\dfrac{1}{2}\times6\ \dfrac{m}{s^2}\times(4.1\ s)^2=50.43\ m.$$