Car slowing from given speed to rest in given time.

[thschica]

A car slows down from a speed of 26.0 m/s to rest in 4.50 s. How far did it travel in that time?
What equation do i use?

 

[HallsofIvy]

Given only the information here, no formula will work. I imagine that you are expected to assume that the car slows down with constant acceleration.

If the car slows from 26.0 m/s to rest (0 m/s) in 4.5 s then its acceleration is (0- 26)/4.5= -5.78 m/s² (notice the negative- that important!).

Do you know the formula s= (1/2)at²+ v₀t? You were given the time, t, and the initial speed v₀ and you now know the acceleration, a.

Actually, that's the "hard" way- for this problem you can use the fact that, with a constant acceleration, the "average" speed is just the average of the initial and final speeds. What is the average of 26.0 and 0? If you go at that average speed for 4.5 seconds, how far do you go? Do the problem both ways and compare the answers!

 

[quicknote]

To calculate the distance traveled by the car in 4.50 seconds, we can use the equation:

d = (vi + vf)/2 * t

where d is the distance, vi is the initial velocity, vf is the final velocity, and t is the time.

Plugging in the given values, we get:

d = (26.0 m/s + 0 m/s)/2 * 4.50 s = 58.5 m

Therefore, the car traveled a distance of 58.5 meters in 4.50 seconds while slowing down from a speed of 26.0 m/s to rest. This calculation assumes that the car decelerated at a constant rate and did not experience any external forces.