Question

in a 200 m dash , detailed video analysis indicated tgat a particular sprinter, speed can be modeled as a quadratic function of time at the beginning of a race, reaching a speed of 11.9m/s in 4.10 seconds, and as a linear funtion of time for the remainder of the race. she finishe d the race in 22.2 secods

t1 r1 v1 a1

t2 r2 v2 a2

t3 r3 v3 a3

Answer 1

At time t = 0,

v = 0

And at t = 4.1 s,

v = 4.1 s, v = 11.9 m/s

Since velocity is a quadratic function of time,

At t = 0, v = 0

So, B = 0

At t= 4.1 , v = 11.9

So,

A = v/t^2 = 11.9/4.1^2 = 0.7079

So,

The displacement is given by

The acceleration is given by

For the remaining time,

We have a = dv/dt = A

At t = 4.1 s,

a = 5.18 m/s^2

So,

A = 5.18

At t = 4.1 s,

v = 11.9 m/s

So,

b = 11.9-5.18*4.1 = -9.338

At t = 22.2 s

The tabular column is given below

	1	2	3
t	0	4.1	22.2
r	0	16.263	200
v	0	11.9	18.7
a	0	5.18	5.18