Section 1: Answers

Hey, guys.
Section One is all about motion in a single dimension.

Key terms: acceleration, velocity, displacement.
Key equations = vf=vi


Answers – Section 1

1. (a) 10 m/s.
(b) 161 s


2.(a) If you double x, you double y.
(b) If you halve x, you halve y.
(c) a straight line through the origin.

3.(a) If you double x, y goes up by a factor of 4.
(b) If you halve x, y is reduced by a factor of four.
(c) A plot of y as a function of
(i) x is a parabola;
(ii) the square of x is a straight line through the origin.

4.(a) 30 m.
(b) 60 m.

5.(a) 20 m.
(b) 80 m.
(c) 28 m
(d) 96 m.

6.(a) 20 m/s ^2.
(b) 80 m.

7. 108.

8. 0.454 s.

9.(a) v i = 5 m/s.
(b) 5/3 m/s ^2.
(c) 7.5 m.

10. the result is shown in this graph:




11.(a) 4.0 s.
(b) 16 ft.
(c) 320 ft.
(d) 21.3


12.The magnitude 10 m/s , to the right at t = 1.0 s , to the left at t = 5.0 s

13. (a) From t = 0 to t = 1.0 s, a = 10 m/s ^2.
From t = 1.0 s to 2.0 s, a = 0.
From t = 2.0 s to 3.0 s, a = -15 m/s ^2.
From t = 3.0 s to 4.0 s, a = 0.
From t = 4.0 s to 5.0 s, a = -15 m/s ^2.

(b) From t = 0 to t = 1 s, x(1s) = 10 m.
From t = 1 to t = 2 s. x(2s) = 25 m.
From t = 2 to t = 3 s. x(3s) = 32.5 m.
From t = 3 to t = 4 s. x(4s) = 32.5 m.
From t = 4 to t = 5 s. x(5s) = 25 m.

(c) From t = 0 to t = 1 s, the slope and velocity are positive and increasing.
From t = 1 to t = 2 s, the slope and velocity are constant and positive.
From t = 2 to t = 3 s, the slope and velocity are positive, but decreasing.
From t = 3 to t = 4 s, the slope and velocity equal zero.
From t = 4 to t = 5 s, slope and velocity are negative, but increasing.

14.(a) vo = 30 m/s
(b) v(2.0s) = 10 m/s
(c) y = 45 m

15.(a) v = -40 m/s,
(b) t = 2 s.
(c) t = 6 s.

16.(a) a = -2.5 m/s ^ 2.
(b) t = 4.0 s.
(c) and (d) are shown in the figure below.



17. yo = 20 m. on the tenth floor.


18.(a) 2.0 s.
(b) 4.0 m.
(c) -8.0 m/s.

19.(a) t = 1 s, the velocity is zero and acceleration is positive
(b) t = 1 s, the velocity is zero. For t > 1s, the acceleration is negative
(c) t = 1 s, the velocity is negative and acceleration is positive
(d) t = 1 s, the velocity is negative and acceleration is negative
(e) t = 1 s, the speed is increasing for all cases except (c).