How to Calculate Distance and Speed with Constant Acceleration

AI Thread Summary
To calculate the distance and speed of a car accelerating from rest to catch up with a truck moving at a constant speed of 22 m/s, the key equations involve the car's acceleration and the truck's constant velocity. The car accelerates at 3.55 m/s², and the position of both vehicles can be expressed as functions of time. The car's position is given by s = 1/2 at², while the truck's position is s = V0t, where V0 is 22 m/s. By equating the two positions and solving for time, the car's distance when it passes the truck can be determined. A graphical representation may help clarify the relationship between time and position for both vehicles.
sydneyfranke
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Homework Statement


A car is at a stop light, when the light turns green a truck blows through the intersection at 22 m/s, and remains constant. The car begins to accelerate (assume at the exact same time as the truck goes through intersection) at a rate of 3.55 m/s/s.
A) How far away from its initial point is the car when it passes the truck?

B) How fast is the car going?


Homework Equations


I would think something like v2= Vo2 + 2a(x-xo) because time is not given. But this doesn't seem right.


The Attempt at a Solution


I have tried the above equations. We just learned this stuff today so I'm still not sure what "Vo" actually is.

If someone could give me the "dumb" version of how to figure this one out, I would greatly appreciate it.
 
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You might need to calculate 't' the time the car catches the truck.
Consider s = v0t + 1/2 at^2

v0 is the intitial speed, so for the truck it is 22m/s and for the car=0
They obviously meet when 's' and 't' are the same - ie they are at the same place at the same time
 
okay, but if a of the truck is 0, won't that cancel out the t^2? I'm still a little confused here.
 
Yes - for the truck it's position at any time 't' is just s = V0 t
For the car it is s = 1/2 a t2 since V0 is 0

Note there is a second solution at time t=0, where they meet at the start - but you aren't interested in that!

Hint: you could draw a simple time against position graph for each vehicle on a piece of graph paper to give you an idea of the answer.
 
Okay, so I have t at 12.39 sec., do I plug that into Vot + 1/2 at2 ? That gives me 545 m, but that just doesn't seem reasonable.
 
22m/s is about 50mph
0-60 in 12.5 secs is reasonable
So you probably aren't an order of magnitude out

Sketch the graph if you aren't sure
 
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