1. A car is wating at a red light. when the light turns green the car starts acc

Question

1. A car is wating at a red light. when the light turns green the car starts accelerating at a constant rate. The distance the car has traveled in feet ( t ) seconds after the light turned green is given by the equation D(t)=3t^2+5t

Please Explain all Steps and show all work: (ANSWER ALL OF THE QUESTIONS 4 TOTAL)(please be clear in handwriting if writing by hand)

a) find a formula for the cars instantaneous velocity?.

b.) what is the cars instantaneous velocity at t=5 seconds?

c.) Acceleration is defined to be the change in velocity over time. Using your answer from part a, find a formula for the cars instantaneous acceleration.

d.) what is the cars instantaneous acceleration at t=3 seconds and at t=6 seconds? does this make sense based on what was stated in the beginning of the problem?

Explanation / Answer

D(t)=3t^2+5t

a) intantanous velocity is dD/dt

D(t)=3t^2+5t, differentiate with respect to time t

dD/dt =3*2t +5*1

dD/dt =6t +5

b)instantaneous velocity at t=5 seconds =6*5 +5

instantaneous velocity at t=5 seconds =35 ft/s

c) instantaneous acceleration =d2D/dt2

d2D/dt2=6*1 +0

d2D/dt2=6 ft/s2

d)instantaneous acceleration at t=3 seconds=6 ft/s2

instantaneous acceleration at t=6 seconds =6 ft/s2

instantaneous acceleration is constant

yes,in the problem it is mentioned car accelerating at a constant rate.

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