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?
To find the distance the car has traveled when it passes the bus, we need to determine the time it took for the car to catch up with the bus.
Let's break down the problem into smaller steps:
Step 1: Determine the time it takes for the car to catch up with the bus.
First, we need to find the time it takes for the car to reach the same speed as the bus. We can use the equation of motion:
v = u + at
where:
v = final velocity (bus velocity) = 16.0 m/s
u = initial velocity (car velocity) = 0 m/s
a = acceleration = 0.5 m/s^2
t = time
Since the car starts from rest, we can rewrite the equation as:
t = (v - u) / a
Substituting the values:
t = (16.0 m/s - 0 m/s) / (0.5 m/s^2)
t = 32 seconds
So, it takes the car 32 seconds to reach the velocity of the bus.
Step 2: Use the time to find the distance traveled by the car.
To find the distance the car has traveled when it catches up with the bus, we can use the equation of motion:
s = ut + (1/2)at^2
where:
s = distance
u = initial velocity (0 m/s)
t = time (32 seconds)
a = acceleration (0.5 m/s^2)
Substituting the values:
s = 0 m/s * 32 s + (1/2) * 0.5 m/s^2 * (32 s)^2
s = 0 m + 0.5 m/s^2 * 16 m^2/s^2
s = 8 meters
Therefore, when the car passes the bus, it has traveled a distance of 8 meters down the road.
d = 16 t
d = (1/2) (.5) t^2 = .25 t^2
so
16 t = .25 t^2
t = 0 as we know
.25 t = 16
t = 64 seconds
d = 16*64 = 1024 meters