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?
d = m

Explanation:

Step1: Set distance equations

Automobile: $d = \frac{1}{2} a t^2$ (starts from rest, $u=0$)
Truck: $d = v t$ (constant speed)

Step2: Equate distances and solve t

$\frac{1}{2} a t^2 = v t$ → $t = \frac{2v}{a}$
Substitute $a=2.40\ \text{m/s}^2$, $v=15.1\ \text{m/s}$: $t = \frac{2×15.1}{2.40} ≈12.58\ \text{s}$

Step3: Calculate overtaking distance

$d = v t = 15.1×12.58 ≈190\ \text{m}$

Answer:

190