At the instant the traffic light turns green, a car that has been waiting at the intersection starts ahead with a constant acceleration of 3.20 m/s^2. At the same instant a truck, travelling with a constant speed of 20.0m/s, overtakes and passes the car. How far beyond its starting point, in metres, does the car overtake the truck?
Please explain your answer and formula used.
When the traffic light turns green, a car that has been waiting at the intersection starts with a constant acceleration of 3.2 m/s^2. At the same instant it is overtaken by a truck moving at a constant speed of 20 m/s.
Let the distance covered before the car overtakes the truck be D. The time taken by the truck to travel D m is given by the formula T = D/V where D is the distance traveled by the truck in time T moving at V m/s.
T = D/20
The distance traveled by an object in t seconds, if the initial speed is u and the acceleration a is given by d = u*t + (1/2)*a*t^2.
For the car, u = 0 m/s and a = 3.2 m/s^2. The car travels a distance D in time D/20. Substituting these values in the formula provided earlier gives:
`D = 0 + (1/2)*3.2*(D/20)^2`
=> 800D = 3.2D^2
=> D = 250
The car overtakes the truck after 250 meters.