Question

An object moving at 1 m/s with distance to target at t=0 of 1000 meters. The object travels at a constant 1 m/s. After each second there is a uniform, instantaneous stretch of 1 km. I.e. after the 1st stretch the object is 2 meters from origin, and 1998 m from target.

(a). Using series/sequences, find the time it takes to reach the target, if the target can be reached.

(b). With a new velocity of 4 m/s, how long would it take the object to reach the target?

Hints provided with question:

1. Understand exactly why the object is 1998 meters away after the first stretch.

2. It will likely help to then set up a sequence where dn is the distance between the object and the target after n seconds but BEFORE the stretch. (i.e. d0 = 1000, d1 = 999 etc.)

Answer 1

Speed of the object is 1 m/sec therefore it covers a distance of 1 meter per second also there is a stretch of 1m after every second hence, we can say that after 1st second object has travelled 1 + 1 = 2 m, after 2 seconds object has travelled 2 +1 +1 = 4 m and so on which means the effective speed of the object is 2 m/s or after n seconds object has travelled 2n meters therefor we put 2n = 1000 gives us n = 500 seconds

After 500 seconds or, 8 min 20 sec the object reaches target.

In second case speed is 4m/sec means object travelles 4 + 1 meters per second hence after n seconds object is 5n meters away from starting point so we put,

5n = 1000 gives us n = 200 seconds

Hence object takes 200 seconds to reach destination or 3 min 20 seconds.