Question

Anna and Bonnie are located on a straight line in the following way: Anna is standing at the origin of the x-axis and when Bonnie is located 20 m away in the positive x direction, running at the constant speed of 4.6m/s toward Anna, Anna begins running toward Bonnie with a constant acceleration of 1.8m/s2 .

(a) Using the diagram below, provide all information given (i.e. Anna’s and Bonnie’s initial velocities and accelerations, marking any vectors in the diagram corresponding to their magnitudes and orientations. Continue to use this diagram through the problem, filling in new information as you calculate it and find it useful (in particular, mark the final location, velocities and accelerations, the times it took each to reach this final point).

(b) Where do Anna and Bonnie meet? What are their velocities, accelerations at that moment, and how long did it take each to reach this point?

(c) What is the distance traveled by each between the start point and the point where they meet? Think about the numbers! Why does Anna travel a smaller distance than Bonnie in the same time?

(d) When do they both have the same speed? Where is each located when they have the same speed?

(e) How much time does it take Anna to reach the 20m mark? How much time does it take Bonnie to reach the origin? How fast is Anna when she reaches the 20m- 4 mark?

(f) Draw an x-t, velocity-time and acceleration-time diagram for both runners (represent these curves for both runners in the same graph)

Answer 1

a)

b)

let they meet after travelling for time "t"

distance travelled by anna = D_a = V_i t + (0.5) a t² = 0 t + (0.5) (1.8) t²

D_a = 0.9 t²                     Eq-1

distance travelled by Bonnie = D_b = V_b t = 4.6 t                 eq-2

D_a + D_b = 20

0.9 t² + 4.6 t = 20

t = 2.81 sec

position of meeting :: X_a = 0.9 t² = 0.9 (2.81)² = 7.11 m

velocity of anna at that point : V = V_i + a t = 0 + 1.8 x 2.81 = 5.06 m/s

acceleration of anna = 1.8 m/s²

velocity of bonnie remains same = V_b = 4.6 m/s

acceleration of bonnie = 0 m/s²

time taken by each = t = 2.81 sec

c)

distance travelled by anna = 7.11 m

distance travelled by bonnie = 20 - 7.11 = 12.89

anna travel a smaller distance since it starts from rest.

d)

let at time "t" they both have same speed

speed of anna , V = 1.8 t

speed of bonnie = 4.6

so 1.8 t = 4.6

t = 2.56 sec

anna's location :X_a = 0.9 t² = 0.9 (2.56)² = 5.89 m

bonnie's location : 20 - 4.6(2.56) = 8.224 m