Marie is the star runner on her track team?

Marie is the star runner on her track team. She runs that last 400 meters of a 1600-meter relay race. An analyst studied film of a race she was in and came up with a formula to describe the distance Marie had run at a given time in the race.





M(t) = (0.1t^2) + 3t





Was there an instant when Marie was going exactly 10 meters per second? If so, when was that instant?|||Is this calculus?





If so, the derivative of a distance equation will be a rate of change, or distance per second, or velocity equation.





M'(t) = 0.2t +3, since there is a t component, that means her velocity is dependent on time, so she is accelerating thru out the run. This is actually unlikely in a real race, but we will assume it is true here.





So if she is going 10 m/s, you would have





10 = 0.2t + 3





0.2t = 10 - 3 = 7





t = 7/0.2 = 35





At 35 seconds, she is going 10 m/s|||You did not say what t represents in M(t). Yes it is the first letter in the word "time" but time for what.





The rate at which Maria was running is found by computing dM(t)/dt = 0.2t + 3. This implies that Maria was increasing her speed during the race. She started her leg of the race at t = 0 going 3 m/sec and got faster as time increased.





For this rate to be 10 m/sec, t must be the solution for 0.2t + 3 = 10.


Which is t = 7/0.2 = 35.





How long did it take Maria to complete her leg of the race? If it took at least 35 seconds, then at that point she was running at 10 m/sec