Andrea, a 59.0 kg sprinter, starts a race with an acceleration of 3.900 m/s2. If she accelerates at that rate for 12.00 m and then maintains that velocity for the remainder of a 100.00 m dash, what will her time (in s) be for the race

her total time taken for the race is 11.58 s

Explanation:

mass of the sprinter, m = 59 kg

acceleration of the sprinter, a = 3.9 m/s²

initial distance covered by the sprinter, d₁ = 12 m

Time taken to cover the first 12 m;

d₁ = ut + ¹/₂at²

where;

u is her initial velocity = 0

d₁ = ¹/₂at²

2d₁ = at²

The velocity of the sprinter at the end of the 12 m;

v = u + at

v = 0 + at

v = at

v = 3.9 x 2.48

v = 9.67 m/s

The last distance covered by the sprinter at the constant velocity of 9.67 m/s = (100 - 12)m = 88 m

The time taken to cover 88 m with an initial velocity of 9.67 m/s is calculated as;

d₂ = vt + ¹/₂at²

Since the velocity is constant, the acceleration, a = 0

d₂ = vt₂

t₂ = d₂/v

t₂ = 88 / 9.67

t₂ = 9.1 s

The total time taken for the race = t₁ + t₂

                                                       = 2.48 s  +  9.1 s

                                                        = 11.58 s

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.