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).