• A car is initially traveling at 50.0 km/h. The brakes are applied and the car stops over a distance of 35 m. What was magnitude of the
car's acceleration while it was braking?

Explanation:

The equation for acceleration is

where vf is final velocity, v0 is initial velocity and t is time in seconds. But we have a problem here because the initial velocity is given in km/hr while the distance is given in meters. We are going to change 50.0 km/hr to m/sec:

which gives us an initial velocity of

v = 13.9 m/s

But that still doesn't give us anything for the time, which is the denominator of the acceleration equation. We have to find it. Since this is one-dimensional travel, use d = rt to find the time it took for the car to travel 35 meters at a rate of 13.9 m/s:

35 = 13.9t and

t = 2.5 seconds. Now we can use that in the acceleration equation:

so

a = -5.6 m/s/s The negative sign tells us that the car is slowing down, as we would expect it to be when it is traveling at a certain rate and eventually stops.