10. The motion of a particle is described by the position function s(t) = 2t² – 15t² +33t+17, t>0, where ț is measured in seconds and s(t) in meters.a. When is the particle at rest?b. When is the velocity positive? -c. Draw a diagram to illustrate the motion of the particle in the first 10 seconds.11. A snowball melts so that its surface area decreases at a rate of 0.5 cm?/min. Find the rateat which the radius decreases when the radius is 4 cm. (SA=4ar?)-12. Brent is driving west at 60 km/h and Aaron is driving south at 70 km/h. Both cars areapproaching the intersection of the two roads. At what rate is the distance between thecars decreasing when Brent's car is 0.4 km and Aaron's is 0.3 km from the intersection?-13. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2m³/min. Find the rate at which the water level is rising when there is 8T m³ of water.14. For the function f(x)= ax? + bx? – 5x + 9, determine the values of a and b so that f (-1)= 12 and f (-1) =3.415. Determine the equations of two lines that pass through the point (-1, -3) and are tangentto the graph of y=x² + 1+16. Two particles have positions at time t given by s1 = 4t – t'and s2 = 5t2 – t3 . Find thevelocities V and V2at the instant the accelerations of the two particles are equal.e 6. Give one example of a rate that is decreasing and one example of a rate that is increasing.7. When a vehicle is said to be travelling at -35 km/h, what does this infer?dv8. If V represents the volume of an object, what doesrepresent? e9. A construction worker accidently drops a hammer from a height of 90 m while workingon the roof of a new apartment building. The height, s, in meters, of the hammer after tseconds can be modelled by the function s(t)=90-4.0t?,t > 0.a. Determine the velocity at 1 s and 4 s. eb. When will the hammer hit the ground? ec. Determine the impact velocity of the hammer.

Name: 10. The motion of a particle is described by the position function s(
Uploaded: 2024-03-05T11:52:21.000Z
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Description: 10. The motion of a particle is described by the position function s(t) = 2t² – 15t² +33t+17, t>0, where ț is measured in seconds and s(t) in meters.a. When is the particle at rest?b. When is the velocity positive? -c. Draw a diagram to illustrate t