Where Will the Car Overtake the Truck?

[mbecker19]

At the instant the traffic light turns green, a car starts with a constant acceleration of 1.3 m/s2. At the same instant a truck, traveling with a constant speed of 3.4 m/s, overtakes and passes the car. How far beyond the traffic light will the car overtake the truck?

 

[rl.bhat]

At the instant of overtake, the relative velocity of truck with respective of car is 3.4 m/s. At the instant of car overtaking the truck, the relative velocity of truck with respective of car will be zero. Using the kinamatic equation find the distance.

 

[Mentallic]

At the instant of car overtaking the truck, the relative velocity of truck with respective of car will be zero.

If this means the car and truck will be traveling at the same speed at point of overtake, I beg to differ.


The car is traveling at constant velocity and the truck is accelerating uniformly. You need 2 kinematic equations that relate these 2 constants and both involve the variable distance.

i.e.

for the truck, use:
$$s=vt$$
s=distance
v=velocity
t=time

for the car, use:
$$s=ut+\frac{1}{2}at^2$$
u=intial velocity
a=acceleration

You will have 2 equations with the 2 variables distance and time. Just manipulate mathematically to find the distance.

 

[matt_crouch]

the equations are the other way round arent they?
its the truck that has the constant speed and the car that has the constant acceleration so like mentallic said use the two equations simultaniously to solve the variables
just the other way round =]

 

[Mentallic]

Oh yeah the other way round. Thats sloppy reading on my part

 

[rl.bhat]

If this means the car and truck will be traveling at the same speed at point of overtake, I beg to differ.
QUOTE]

At the starting point the car is at rest and truck is moving with a constant velocity.So at the starting point their relative velocity will be equal to 3.4 m/s. Car accelerates and its velocity increases. At some point its velocity must be equal to the velocity of the truck. At that instant their relative velocity will be zero. Since the relative velocity decreases, we can use negative acceleration.
Use v^2 = u^2 - 2as to find s.

 

[Delphi51]

The car will first match the velocity of the truck, then continue to accelerate until its velocity exceeds that of the truck before passing it. There are two interesting times.