say x = 0 at start, t = 0
x = 80 at t = 7
v = 15 at x = 80 and t = 7
v = Vo + a t
x = 0 + Vo t + .5 a t^2
so
15 = Vo + 7 a
80 = Vo (7) +.5 a (49)
solve those two equations for Vo and a
What is the antelope's velocity at the first point?
What is the acceleration ?
x = 80 at t = 7
v = 15 at x = 80 and t = 7
v = Vo + a t
x = 0 + Vo t + .5 a t^2
so
15 = Vo + 7 a
80 = Vo (7) +.5 a (49)
solve those two equations for Vo and a
velocity = initial velocity + acceleration times time
or
v = Vo + a t
position = initial position + initial velocity times time + half of acceleration times time squared
or
x = Xo + Vo t +(1/2) a t^2
here I called Xo, initial position zero and x after 7 seconds was 80
so
80 = 0 + Vo (7) + (1/2) a (7)^2
and I know final velocity at t = 7 is 15 but I do not know Vo
so
15 = Vo + a (7)
The equation is:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
We are given that the antelope covers a distance of 80 meters in 7 seconds and its velocity at the second point is 15 meters per second.
First, let's calculate the acceleration. We can use the equation:
a = (v - u)/t
Substituting the given values:
a = (15 m/s - u)/7s
Next, to find the antelope's velocity at the first point, we'll use the equation:
80m = ut + (1/2)at^2
Since it starts from rest at the first point, the initial velocity (u) will be 0.
Substituting these values into the equation:
80m = 0 + (1/2)a(7s)^2
80m = (49/2)as^2
160m = 49as^2
Now we have two equations:
a = (15 m/s - u)/7s
160m = 49as^2
To solve these equations, we can substitute the value of a from the first equation into the second equation and solve for u.
160m = 49((15 m/s - u)/7s)s^2
160m = 7s^2(15 m/s - u)
160m = 105s^2 - 7s^2u
Simplifying:
7s^2u = 105s^2 - 160m
u = (105s^2 - 160m)/(7s^2)
Now we can substitute the given values of s and m to find the value of u.
Finally, we have the antelope's velocity at the first point (u) and the acceleration (a).