Question

At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.40 m/s^2. At the same instant, a truck, traveling with a constant speed of 15.5 m/s, overtakes and passes the automobile.
How far beyond its starting point does the automobile overtake the truck?

How fast is the automobile traveling when it overtakes the truck?

Answer 1

Answer

given,

Initial speed of the car = 0 m/s

acceleration of car = 2.4 m/s²

Speed of the truck = 15.5 m/s

to car to overtake the truck distance travel by both should be same

distance traveled by the truck

d = 15.5 t

distance traveled by the car

d = u t + 1/2 gt ²

d = 0.5 x 9.8 t²

now, equating both the equations

15.5 t = 4.9 t²

t = 3.163 s

Time taken by car to overtake truck is 3.163 s

distance travel by the car = 15.5 x 3.163

d = 49 m

b) Speed of the automobile

using equation of motion

    v = u + at

    v = 0 + 2.4 x 3.163

    v = 7.59 m/s

Speed of the automobile while crossing truck is equal to v = 7.59 m/s