Thread: Catching a Bus

Jodi's bus leaves at 5:30pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has departed.

(a) Find parametric equations that describe the motion of the bus and Jodi as a function of time.

(b) Determine algebraically whether Jodi will catch the bus. If so, when?

HINT GIVEN FOR PART (a):

The position s at time t of an object having acceleration a is s = (1/2) * (at^2)

Jodi's bus leaves at 5:30pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has departed.

(a) Find parametric equations that describe the motion of the bus and Jodi as a function of time.

equations will be

Sb(displacement of bus)= (1x3xt^2)/2........as given in hint from 2nd
equation of motion

Sj (displacement of Jodi)= 5 (t-2) .
.....as jodi starts 2 seconds late and has constant velocity

(b) Determine algebraically whether Jodi will catch the bus. If so, when?
for catching the bus the two displacements need to be equal
so equate them if you get a real solution then jodi will be in bus
else he misses it..
the second case would happen..

Originally Posted by ADARSH

Jodi's bus leaves at 5:30pm and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has departed.

(a) Find parametric equations that describe the motion of the bus and Jodi as a function of time.

equations will be

Sb(displacement of bus)= (1x3xt^2)/2........as given in hint from 2nd
equation of motion

Sj (displacement of Jodi)= 5 (t-2) .
.....as jodi starts 2 seconds late and has constant velocity

(b) Determine algebraically whether Jodi will catch the bus. If so, when?
for catching the bus the two displacements need to be equal
so equate them if you get a real solution then jodi will be in bus
else he misses it..
the second case would happen..

Wonderfully explained.