Answer:
A) The speed at the first point is 6.91 m/s.
B) The acceleration is 1.12 m/s²
Explanation:
The equations of velocity and position of the antelope will be as follows:
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) If we place the origin of the frame of reference at the first point, we can say that at t = 6.60 the position of the antelope is 70.0 m and its velocity is 14.3 m/s. In this way, we will have 2 equations with 2 unknowns, the initial velocity (the velocity at the first point) and the acceleration.
Let´s start finding the speed at the first point:
v = v0 + a · t (solving for "a")
(v - v0)/t = a
Replacing a = (v - v0)/t in the equation of the position:
x = x0 + v0 · t + 1/2 · (v - v0)/t · t² (x0 = 0)
x = v0 · t + 1/2 · v · t - 1/2 · v0 · t
x - 1/2 · v · t = 1/2 · v0 · t
2/t · (x - 1/2 · v · t) = v0
2/6.60 s · (70.0 m - 1/2 · 14.3 m/s · 6.60s) = v0
v0 = 6.91 m/s
The speed at the first point is 6.91 m/s.
B) Using the equation of velocity
a = (v - v0)/t
a = (14,3 m/s - 6.91 m/s) / 6.60 s
a = 1.12 m/s²
The acceleration is 1.12 m/s²
