A certain vehicle can accelerate from a standing start to a speed of v(t) = -0.24t (for 0 st < 30). 14t feet per second after t seconds (a) Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.] D(t) = (b) Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.) D(10) = [ | ft

Q: 3. The number of sales per day S(t), measured in thousands, of a new toy is found to be 400 t+25…

A: Need to answer the following parts for the given sales function with respect to the number of days.

Q: 2. From 2007 to 2014, there was a dramatic increase of smartphone sales. The number of smartphones…

A: Given:- The number of smartphones in millions sold to end users from 2007 to 2014 is modeled by the…

Q: 4. The duck population near a small lake can be modelled by the d(t) = 0.5(t² + 8) (t + 4) Where t…

A: given that , duck population function is given by :-d(t) = 0.5(t2+8)(t+4)where  t is time in years…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.