A runner whose initial speed is 29 km/hr increases her speed to 31 km/hr in order to win a race. If the runner takes 0.5 seconds to complete this increase in speed, what is her acceleration?
I think it's either 1440 km/hr/hr
or 0.4 km/hr/sec. Are you supposed to convert the seconds? Thank you in advance.
This involves the acceleration formula.
a = change in velocity/change in time
change in velocity = 31000 m/hr/3600 s/hr - 29000m/hr/3600 s/hr = .56 m/s
so
.56 m/s / .5 s = 1.11 m/s^2
a= (31km/hr - 29km/hr) / 5sec
a= 0.4 km/hr/s
That's how I got one of the answers....I am confused at what you are trying to show me.
a= (Vf - Vi) / t
To find the runner's acceleration, we can use the formula:
acceleration = change in velocity / time taken
The change in velocity can be calculated by subtracting the initial velocity from the final velocity:
change in velocity = final velocity - initial velocity
Given that the initial velocity is 29 km/hr and the final velocity is 31 km/hr, we have:
change in velocity = 31 km/hr - 29 km/hr = 2 km/hr
Next, we need to convert the time taken from seconds to hours. Since the initial and final velocities are given in km/hr, it is more convenient to have the time in hours as well.
The time taken is 0.5 seconds. To convert it to hours, we divide by the number of seconds in an hour (3600 seconds):
time taken (in hours) = 0.5 seconds / 3600 seconds/hr ≈ 0.00014 hr
Now, we can calculate the acceleration:
acceleration = change in velocity / time taken
= 2 km/hr / 0.00014 hr
≈ 14285.71 km/hr/hr
Therefore, the runner's acceleration is approximately 14285.71 km/hr/hr.
So, your initial guess of 1440 km/hr/hr is close, but not quite correct. And your second guess of 0.4 km/hr/sec is incorrect because the units need to match, either km/hr/hr or km/hr/sec.