Can I get an explanation for those questions

21. Particle Motion A particle moves along a line so that its position at any time / 2 0 is given by the function s(1) (1 - 2) (1 - 4) where's is measured in meters and t is measured in seconds. (a) Find the instantaneous velocity at any time t. (b) Find the acceleration of the particle at any time t. (c) When is the particle at rest? (d) Describe the motion of the particle. At what values of / does 12 the particle change directions? 22. Particle Motion A particle moves along a line so that its position at any time t 2 0 is given by the function s(t) = 612 + 81 + 2 where s is measured in meters and t is measured in seconds. gine stopped? (a) Find the instantaneous velocity at any time t. (b) Find the acceleration of the particle at any time t. hat was its (c) When is the particle at rest? (d) Describe the motion of the particle. At what values of t does the rocket the particle change directions? 23. Particle Motion The position of a body at time t sec is e opened? s = 1' - 612 + 91 m. Find the body's acceleration each time the en was the velocity is zero. 24. Finding Speed A body's velocity at time t sec is v = 273 - 912 + 121 - 5 m/sec. Find the body's speed each time the accel- eration is zero. 25. Draining a Tank It takes 12 hours to drain a storage tank by hat its posi- opening the valve at the bottom. The depth y of fluid in the tank t hours after the valve is opened is given by the formula y = 6(1 - 5m. onds. (a) Find the rate dy/ di (m/h) at which the water level is chang- ing at time t. (b) When is the fluid level in the tank falling fastest? slowest? What are the values of dy/dt at these times? (e) Graph y and dy/ di together and discuss the behavior of y in relation to the signs and values of dy/ di.10 min? 9. Particle Motion The accompanying figure shows the velocity 12. Thoroughbr v = f(t) of a particle moving on a coordinate line. race. (A furlo (a) When does the particle move forward? move backward? seconds as ou speed up? slow down? furlong marke (b) When is the particle's acceleration positive? negative? zero? the beginning (c) When does the particle move at its greatest speed? (d) When does the particle stand still for more than an instant? F 0 20(e) During fastest? e number line shown 13. Lunar Projectile Motion A rock thrown vertically upward (a) How fast was the (b) shows the posi- from the surface of the moon at a velocity of 24 m/sec (about (b) For how many se 86 km/h) reaches a height of s = 24t - 0.8t meters in t (c) When did the ro seconds. velocity then? s (cm) (a) Find the rock's velocity and acceleration as functions of (d) When did the time. (The acceleration in this case is the acceleration of falling then? gravity on the moon.) (e) How long did (b) How long did it take the rock to reach its highest point? (f) When was the (c) How high did the rock go? acceleration [sec) (d) When did the rock reach half its maximum height? (e) How long was the rock aloft? 14. Free Fall The equations for free fall near the surfaces of Mars 19. Particle Moti and Jupiter (s in meters, t in seconds) are: Mars, s = 1.8612; tion at any tim Jupiter, s = 11.442. How long would it take a rock falling from right? standing rest to reach a velocity of 16.6 m/sec (about 60 km/h) on each planet? where s is m (a) Find the