Question

A sprinter runs a 100 metre race. He does not move for 0.2 seconds after the...

A sprinter runs a 100 metre race. He does not move for 0.2 seconds after the starting pistol is fired. Then his velocity vms-1 increases as v(t) = -0.5t2 + 5t - 0.98 where t is time in seconds. he reaches his maximum speed and maintains this until he crosses the finish line.

Calculate his time to complete the race.

Homework Answers

Answer #1

when velocity is maximum

dv/dt = 0

-0.5*2*t + 5 - 0 = 0

-1*t = -5

t = 5

distance travelled in the first 5 s,

d1 = integral v*dt ( t = 0 to t = 5s)

= integral (-0.5*t^2 + 5*t + 0.98)*dt

= -0.5*t^3/3 + 5*t^2/2 + 0.98*t

= -0.5*(5^3 - 0^3)/3 + 5*(5^2 - 0^2)/2 + 0.98*(5 - 0)

= 46.57 m

so, velocity after 5 s, v = -0.5*5^2 + 5*5 + 0.9

= 13.4 m/s


remaining distance, d2 = 100 - d1

= 100 - 46.57

= 53.43 m

reaining time taken = d2/v_max

= 53.43/13.4

= 3.987 s

so, total time taken = 0.2 + 5 + 3.987

= 9.187 s <<<<<<<--------------------Answer

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT