Kinematics - Sample Problems & Solutions
1. Relative Motion example:
A little girl sees an ice-cream truck 20 m ahead of her and starts running at 4.0 m/s in an effort to catch it.
The driver, not realizing that the girl is running behind the truck, accelerates away at 1.0 m/s2.
Will the child catch the truck?
Solution 1. Graphical Analysis
Child | Truck | |
d = (v)(t)-20 | Time |
d =1/2(a)(t2) |
V1=4.0 m/s | a = 1.0 m/s2 | |
d (m) | t (s) | d(m) |
-20.00 | 0.00 | 0.00 |
-16.00 | 1.00 | 0.50 |
-12.00 | 2.00 | 2.00 |
-8.00 | 3.00 | 4.50 |
-4.00 | 4.00 | 8.00 |
0.00 | 5.00 | 12.50 |
4.00 | 6.00 | 18.00 |
8.00 | 7.00 | 24.50 |
12.00 | 8.00 | 32.00 |
16.00 | 9.00 | 40.50 |
20.00 | 10.00 | 50.00 |
24.00 | 11.00 | 60.50 |
28.00 | 12.00 | 72.00 |
32.00 | 13.00 | 84.50 |
As we can see from the graph the child (purple straight line) does not meet the truck (orange curve).