Answer:
A)The speed of the antelope at the first point is 2.43 m/s.
B) The acceleration of the antelope is 1.77 m/s²
Step-by-step explanation:
The equations of the position and velocity of the antelope is given by the following expressions:
x = x0 + v0 · t + 1/2 · a ·t²
v = v0 + a · t
Where:
x = position of the antelope at time t
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
v = velocity at time t
A) Let´s place the center of the frame of reference at the first point. The equation of position at t = 7.50 s will be:
x = x0 + v0 · t + 1/2 · a ·t²
68.0 m = 0 m + v0 · 7.50 s + 1/2 · a · (7.50 s)²
We also know that at the second point the velocity is 15.7 m/s. Then at t = 7.50 the velocity will be 15.7 m/s.
v = v0 + a · t
15.7 m/s = v0 + a · 7.50 s
We can solve this equation for "a" and replace it in the equation of height to obtain "v0". Then:
a = (15.7 m/s - v0) / 7.50 s
Replacing it in the equation for position:
68.0 m = 0 m + v0 · 7.50 s + 1/2 · a · (7.50 s)²
68.0 m = v0 · 7.50 s + 1/2 · (15.7 m/s - v0) / 7.50 s · (7.50 s)²
68.0 m = v0 · 7.50 s + 7.85 m/s · 7.50 s - 3.75 s · v0
68.0 m - 7.85 m/s · 7.50 s = 3.75 s · v0
(68.0 m - 7.85 m/s · 7.50 s) / 3.75 s = v0
v0 = 2.43 m/s
The speed of the antelope at the first point is 2.43 m/s.
B) The acceleration of the antelope will be:
a = (15.7 m/s - v0) / 7.50 s
a = (15.7 m/s - 2.43 m/s) / 7.50 s
a = 1.77 m/s²
The acceleration of the antelope is 1.77 m/s²