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/s². at the same instant, a truck, traveling with a constant speed of 15.1 m/s, overtakes and passes the automobile.

part a
how far beyond its starting point does the automobile overtake the truck?

part b
how fast is the automobile traveling when it overtakes the truck?

Explanation:

Step1: Determine overtaking time relation

Automobile distance: \( d = \frac{1}{2}at^2 \); Truck distance: \( d = v_t t \). Equate: \( \frac{1}{2}at^2 = v_t t \Rightarrow t = \frac{2v_t}{a} \)

Step2: Calculate automobile speed

Automobile speed: \( v = at \). Substitute \( t \): \( v = a \cdot \frac{2v_t}{a} = 2v_t \)

Step3: Substitute values

\( v = 2 \times 15.1 = 30.2 \, \text{m/s} \)

Answer:

30.2