At the instant a traffic light turns green, a car starts from rest with a given constant acceleration 0.5 m/s^2. just as the light turns green, a bus, traveling with a given cinstant speed 16.0 m/s, passes the car. The car speeds up and passes the bus some time later. How far down the road has the car traveled when the car passes the bus?

Answer 1

Car:
a(t)=0.5
v(t)=0.5t
s(t)=0.25t^2

all of this information is found from taking the integral of 0.5 and since the integral of the acceleration function is v(t)=0.5t+v(initial) we just substitute the initial velocity with 0 because it's 0. Same thing with initial the position function.

bus:
v(t)=16
s(t)=16t

so with this information you're trying to find when s(t) of the car = s(t) of the bus to find when the car catches up to the bus.

0.25t^2=16t
0.25t^2-16t=0
0.25t(t-64)=0
t=0, 64
t=64s

we just ignore that t=0 because time can't equal 0, and most problems will have two solutions (one negative or one equal to 0) and you will be required to cancel one to find the answer.