At the instant a traffic light turns green, a car starts moving with a constant acceleration a of 4.00 m/s2. At the same instant a truck, traveling with a constant speed of 10.09 m/s, overtakes and passes the car. How far beyond the traffic light will the car overtake the truck?
At the same time a truck, traveling with a constant speed of 9.5m/s, overtakes and passes the automobile. (A) How far beyond the traffic light will the automobile overtake the truck?
Given that,
the car overtakes the truck
therefore their distance covered are equal.
distance covered by the car
x=1/2X4t^2
x=2t^2 -------- (1)
By the truck
x=vXt
ie,x=10.09Xt
50.45
To determine how far beyond the traffic light the car will overtake the truck, we need to find the position of both vehicles at the moment the car overtakes the truck.
Let's break down the problem step by step:
Step 1: Determine the time it takes for the car to overtake the truck
Since the car is accelerating, we can use the kinematic equation:
vf = vi + at
Where:
vf is the final velocity of the car
vi is the initial velocity of the car
a is the acceleration of the car
t is the time
In this case, the car starts from rest (vi = 0), and we want to find the time it takes for the car to reach the same velocity as the truck (vf = 10.09 m/s). Rearranging the equation, we have:
t = (vf - vi) / a
Plugging in the values, we get:
t = (10.09 m/s - 0) / 4.00 m/s²
t = 2.52 seconds
Step 2: Find the distance traveled by the car during the time it overtakes the truck
To find the distance traveled by the car during this time, we use the equation of motion:
d = vit + (1/2)at²
Where:
d is the distance
vi is the initial velocity of the car
t is the time
a is the acceleration of the car
In this case, vi = 0 and a = 4.00 m/s². Plugging in the values, we have:
d = (0)(2.52 s) + (1/2)(4.00 m/s²)(2.52 s)²
d = 6.36 m
Therefore, the car will overtake the truck at a distance of 6.36 meters beyond the traffic light.