Answer:
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
