# Challenging Question

1. Oct 17, 2004

### thomasrules

A car is observed to cross an intersection in 4s. If the intersection is 40 meters wide, and the car accelerated at 3.3m/s^2, calculate its speed when half-way across the intersection.

I have been having a tought time with this problem because I'm not sure what the initial speed is. Also I don't know what the time would be at half. Its confusing, please help

2. Oct 17, 2004

### arildno

1. You know the time when it has travelled 40meters, and the constant acceleration during that period.
Use this info to determine the initial velocity, from the equation giving you the distance travelled as a function of t.
2. Determine the value of "t" when the car has travelled 20 meters (from the same equation for the position).
Insert that value of "t" into your expression for the velocity at time "t".

3. Oct 17, 2004

### thomasrules

what is the equation?

4. Oct 17, 2004

### thomasrules

someone still help explain more i'm still not getting it

5. Oct 17, 2004

### Pyrrhus

Use arildno reasoning with the kinematic equations for uniform acceleration

$$info:$$
$$x_{o} = 0 m$$
$$x = 40 m$$
$$a = 3.3 m/s^2$$
$$t = 4s$$

Using this equation you can get the initial speed

$$x - x_{o} = v_{o}t + \frac{1}{2}at^2$$

Now using the same equation, you can get the time t, with a displacement of 20 m and same acceleration

$$x - x_{o} = v_{o}t + \frac{1}{2}at^2$$

Now using this equation, you can plug in the time t, and find the speed at that time (at 20 m)

$$v = v_{o} + at$$

arildno answer couldn't be any more clear.