Section 2.7 Homework

1. A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet.

$f\left(t\right)=0.01t^4–0.03t^3$

(a) Find the velocity at time t (in ft/s).

(b) What is the velocity after 1 second(s)?

(c) When is the particle at rest?

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)

(e) Find the total distance traveled during the first 9 seconds. (Round your answer to two decimal places.)

(f) Find the acceleration at time t (in

ft/s2).

Find the acceleration after 1 second(s).

(g) Graph the position, velocity, and acceleration functions for the first 9 seconds.

(h) When, for  0 ≤ t < ∞,  is the particle speeding up? (Enter your answer using interval notation.)

When, for 0 ≤ t < ∞,  is it slowing down? (Enter your answer using interval notation.)

2.  The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 24.5 m/s is h = 2 + 24.5t − 4.9

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? 

(c) What is the maximum height?

(d) When does it hit the ground?

(e) With what velocity does it hit the ground?

3.  If a ball is thrown vertically upward with a velocity of 96 ft/s, then its height after t seconds is s = 96t − 16

.

(a) What is the maximum height reached by the ball?

(b) What is the velocity of the ball when it is 128 ft above the ground on its way up? (Consider up to be the positive direction.)

What is the velocity of the ball when it is 128 ft above the ground on its way down?