In a relay race the second runner does not start from rest. it covers 100 m in 10 sec, finishing with maximum velocity of 12 m/sec, assuming the constant acceleration, determine his initial velocity. ??
v = Vo + at
s = Vo*t + 1/2 at^2
12 = Vo + 10a
a = (12-Vo)/10
100 = Vo*10 + (12-Vo)/20 * 100
100 = 10Vo + 5(12-Vo)
100 = 5Vo + 60
Vo = 8
To determine the second runner's initial velocity, we can use the equation of motion that relates distance, time, final velocity, and initial velocity in a straight-line motion with constant acceleration:
vf = vi + at
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
In this case, we are given the following information:
Distance covered (d) = 100 m
Time taken (t) = 10 sec
Final velocity (vf) = 12 m/s
First, let's find the acceleration (a) using the formula:
a = (vf - vi) / t
Given that the acceleration is constant, we assume it remains the same throughout the race. Rearranging the formula to solve for the initial velocity (vi):
vi = vf - at
Using the values we have:
a = (12 m/s - vi) / (10 sec)
Now we need to calculate the acceleration (a). Rearranging the formula:
a = (vf - vi) / t
a = (12 m/s - vi) / (10 sec)
We can substitute this value of acceleration (a) back into vi = vf - at:
vi = 12 m/s - a * 10 sec
And since we already know a = (12 m/s - vi) / (10 sec), we can substitute this expression for a:
vi = 12 m/s - [(12 m/s - vi) / (10 sec)] * 10 sec
Now we can solve this equation for vi. Simplifying:
vi = 12 m/s - (12 m/s - vi)
This equation can be rearranged to solve for vi:
vi + vi = 12 m/s - 12 m/s
2vi = 0
vi = 0
Therefore, the second runner's initial velocity is 0 m/s.