# Mechanics-related car question

1. Nov 1, 2005

### lando45

Hey,

I have been set this question and I thought I'd answered it perfectly but it turns out I haven't:

A person driving her car at 43 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection. The intersection is 15 m wide. Her car can accelerate from 43 km/h to 70 km/h in 8.1 s. Ignore the length of her car and her reaction time. If she hits the gas, how far will she travel before the light turns red?

I decided to use s = ut + ½at² as it seemd the most appropriate, here's what I got:

s = distance travelled = unknown
u = initial speed = 43km/h = 11.944m/s
t = time = 2.0s
a = acceleration = (70km/h - 43km/h) / 8.1s = 3.333m/s/s

s = (11.944 x 2) + (½ x 3.333 x 2.0²)
s = 23.888 + 6.666
s = 30.555m

So I got the distance travelled by the car in the 2 seconds before the light turned red if the driver sped up to be 30.555m but my teacher tells me this is wrong...anyone know why?

Last edited: Nov 1, 2005
2. Nov 1, 2005

### Kamataat

The acceleration is wrong. You need to use the same units for all variables.

- Kamataat

3. Nov 1, 2005

### Kyon

Yes, this is just an error in your units. I didn't pay attention as I thought you did the conversion, but Kamataat is right.

Anyway, accelerating from 43 to 70 km/h in 8.1s is way slower than an acceleration of 3.3 m/s² (i didn't do the math though)

I think just doing the right conversion as Kamataat said should work. Did your teacher give you the correct answer?

Kyon.

4. Nov 1, 2005

### lando45

Ah thanks a lot, I solved it correctly now. Just had to convert the acceleration from 3.333km/h/s to 0.98m/s/s. Thanks again guys.