Question

1. A cat is moving at 18 m/s when it accelerates at 4 m/s^2 for 2 seconds. What is his new velocity?

2.A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s^2. How many seconds are required before the car is traveling 3.0 m/s?

3. A race car is traveling at +76 m/s when it slows down at -9 m/s^2 for 4 seconds. What is his new velocity?

4. A speedboat increases in speed uniformly from 20 m/s to 30 m/s in a distance of 200 m.   What is the acceleration of the speedboat?

5. Julie is walking around a track at a 2 m/s for some exercise. She then decides to start jogging so she accelerates at a rate of 0.5 m/s^2 for 3 seconds. How far did Julie travel from the time she started to accelerate to the end of the 3 seconds?

Answer 1

1)

$$v=v_0+at,$$ $$v=18\ \dfrac{m}{s}+4\ \dfrac{m}{s^2}\times2\ s=26\ \dfrac{m}{s}.$$

2)

$$v=v_0+at,$$ $$t=\dfrac{v-v_0}{a}=\dfrac{3\ \dfrac{m}{s}-22\ \dfrac{m}{s}}{-2.1\ \dfrac{m}{s^2}}=9.05\ s.$$

3)

$$v=v_0+at,$$ $$v=76\ \dfrac{m}{s}+(-9\ \dfrac{m}{s^2})\times4\ s=40\ \dfrac{m}{s}.$$

4)

$$v^2=v_0^2+2ad,$$ $$a=\dfrac{v^2-v_0^2}{2d}=\dfrac{(30\ \dfrac{m}{s})^2-(20\ \dfrac{m}{s})^2}{2\times200\ m}=1.25\ \dfrac{m}{s^2}.$$

5)

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=2\ \dfrac{m}{s}\times3\ s+\dfrac{1}{2}\times0.5\ \dfrac{m}{s^2}\times(3\ s)^2=8.25\ m.$$