Graphs of the position functions of two particles are shown, where t Is measured

Question

Graphs of the position functions of two particles are shown, where t Is measured in seconds. When is the particle in figure (a) speeding up? (Enter your answer using interval notation.) When is the particle in figure (a) slowing down? (Enter your answer using interval notation.) When is the particle in figure (b) speeding up? (Enter your answer using interval notation.) When is the particle in figure (b) slowing down? (Enter your answer using interval notation.) The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level with an initial velocity of 24.5 m/s is h = 4 + 24.5t - 4.9t^2 after t seconds. (Round your answers to two decimal places.) (a) Find the velocity after 2 s and after 4 s. v(2) = m/s v(4) = m/s (b) When does the projectile reach its maximum height? s (c) What is the maximum height? m (d) When does it hit the ground? s (e) With what velocity does it hit the ground? m/s

Explanation / Answer

Particle is accelerating(speeding up/slowing down) when there is change in position wrt time.

And when rate of change of position is higher, particle speeds/slowes down FASTER.

When particle is going away from zero position, it speeds up, slows down while coming to zero position.

So (a) speeding up in interval : 0-1 and 3-4

(b) slowing down in interval :1-3

In between (@3) the particle almost stops for some time as change in position is almost zero.

B:

(a) Speed up in interval : 2-3

(b ) Slows down in interval : 0-2,. 3-4.

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