Question

6. A boat travels 12.0 m while it reduces its velocity from 9.5 m/s to 5.5 m/s. What is the magnitude of the boat’s acceleration while it travels the 12.0 m?

7. A 10-kg crate is pushed across a frictionless surface with a force of 30 N. What is its acceleration?

8. John had an acceleration of 0.35m/s^2. He traveled for 91 seconds with this acceleration. What would John’s final velocity be if he was initially moving at 2.0 m/s?

9.A car’s velocity is given by v (t) = 5 - 10t. Find the average acceleration between t = 2 and t = 5?

10. Given the position s(t)= - 2t^3 + 13t^2, where s is in meters and t is in seconds. Find the average velocity from t = 4 to t = 6.

Answer 1

6. $s=\frac{v^2-v_0^2}{2a}\to a=\frac{v^2-v_0^2}{2s}=\frac{5.5^2-9.5^2}{2\cdot12}=-2.5\ (m/s^2)$

7. $F=ma\to a=F/m=30/10=3\ (m/s^2)$

8. $v=v_0+at=2+0.35\cdot91=33.85\ (m/s)$

9. $a=dv/dt=-10\ (m/s^2)$ or $a_{avr}=\frac{1}{5-2}\int_2^5adt=-10\ (m/s^2)$

10. $v_{avr}=\frac{1}{6-4}\int_4^6vdt=\frac{1}{6-4}\int_4^6|(-6t^2+26t)|dt=22\ (m/s)$