Question

Question 8 (4 points)

Duane and Albert have a race. Duane starts 5 m ahead of Albert and runs forward at a speed of 3 m/s. Albert runs forward at a speed of 4.2 m/s.

a. Write an expression for Duane's position in terms of t and vduane. (Hint: Set x = 0 at Albert's starting point.) (1 point)

a is x=5+3t


b. Write an expression for Albert's position in terms of t and valbert. (1 point)

x=4.2t

c. At what time does Albert catch up to Duane? (Hint: Set the two expressions for position equal to each other and solve for time.) (1 point)

t=4.17 seconds

d. How far from Albert's starting point are they when they meet? (1 point)

i solved a,b, c but donot know how to do d

Answer 1

Answer:

The answer to your question is:

Explanation:

Data

Duane                                          Albert

d = 5 m ;  v = 3 m/s                     v = 4.2 m/s

a)                                                b)

Duane's                                      Albert's

d = 5 + (3)t                                  d = 4.2t

d = 5 + 3t

c)                            5 + 3t = 4.2t

                              4.2t - 3t = 5

                                      1.2t = 5

                                           t = 4.17 s

d)

Duane's

d= 5 + 3(4.17)

d = 17.51 m

Alberts

d = 4.2(4.17)

d = 17.51 m

Answer 2

Answer:

S_d = 5 + 3*t

S_a =  4.2*t

t = 5 / 1.2 = 4.17 s

17.514 m

Explanation:

Given:

- The initial position of Duane s_i = 5

- The speed with which Duane runs v_d = 3 m/s

- The speed with which Albert runs v_a = 4.2 m/s

Find:

a) Write an expression for Duane's position in terms of t and vduane.

b. Write an expression for Albert's position in terms of t and valbert.

c. At what time does Albert catch up to Duane?

d. How far from Albert's starting point are they when they meet?

Solution:

- The position of Duane from start is:

                     S_d = s_i + v_d*t

                     S_d = 5 + 3*t

- The position of Albert from start is:

                     S_a = s_i + v_d*t

                     S_a = 0 + 4.2*t = 4.2*t

- When Albert catches up-to Duane their positions are equal.

                     S_a = S_d

                     5 + 3*t = 4.2*t

                     1.2*t = 5

                     t = 5 / 1.2 = 4.17 s

- The distance at which they meet is governed by time t calculated in part above:

                     S_a = 4.2*(4.17) = 17.514 m