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

d = 1024 m

Explanation:

Kinematics of the car

The car moves with uniformly accelerated movement we apply the following formula:

d = v₀t + (1/2) * a*t² Formula (1)

Where:

d:displacement in meters (m)

t : time in seconds (s)

v₀: initial speed in m/s

a: acceleration in m/s²

Data

v₀₁ = 0 : initial speed of the car

a₁ = 0.5 m/s² : acceleration of the car

Kinematics equation of the car

We replace data in the formula (1):

d = 0 + (1/2) * 0.5*t²

d = (0.25) * t² Equation (1)

Kinematics of the bus

The car moves with uniformly movement (constant speed) we apply the following formulas:

d = v*t Formula (2)

Where:

d:displacement in meters (m)

t : time in seconds (s)

Data

v = 16 m/s

Kinematics equation of the bus

We replace data in the formula (2):

d = 16*t Equation (2)

Problem development

when the car passes the bus the elapsed time (t) and the distance (d) is equal for both.

Equation (1) = Equation (2) = d

(0.25) * t² = 16*t We divide both sides of the equation by t

(0.25) * t = 16

t = 16 / (0.25)

t = 64 s

We replace t in the equation (2)

d = 16*t

d = 16 * (64)

d = 1024 m