An antelope moving with constant acceleration covers the distance between two points 70.0
m apart in 7.00 s. Its speed as it passes the second point is 15.0 m/s. (a) What is its speed at the first
point? (b) What is its acceleration?
Solution
To find the speed of the antelope at the first point, we can use the formula:
v^2 = u^2 + 2as
Where:
v = final velocity (15.0 m/s)
u = initial velocity (unknown)
a = acceleration (unknown)
s = distance (70.0 m)
Since the antelope is moving with constant acceleration, we can rearrange the equation to solve for the initial velocity:
u^2 = v^2 - 2as
Let's calculate it now:
u^2 = (15.0 m/s)^2 - 2 * a * 70.0 m
Now, let's find the acceleration. We can use the formula:
v = u + at
where:
v = final velocity (15.0 m/s)
u = initial velocity (unknown)
a = acceleration (unknown)
t = time (7.00 s)
Rearranging the equation to solve for acceleration:
a = (v - u) / t
Let's calculate it now.
To find the speed of the antelope at the first point, we need to calculate its initial velocity. We can determine the initial velocity by using the equation:
v = u + at
Where:
- v is the final velocity (15.0 m/s)
- u is the initial velocity (which we want to find)
- a is the acceleration of the antelope (which we also want to find)
- t is the time taken (7.00 s)
(a) Finding the initial velocity:
Rearranging the equation, we have:
u = v - at
Substituting the given values, we get:
u = 15.0 m/s - a * 7.00 s
(b) Finding the acceleration:
To calculate the acceleration, we can use the equation:
s = ut + (1/2)at^2
Where:
- s is the distance covered (70.0 m)
- u is the initial velocity (which we will obtain from part (a))
- t is the time taken (7.00 s)
- a is the acceleration (which we also want to find)
Rearranging the equation, we have:
a = 2(s - ut) / t^2
Substituting the known values, we get:
a = 2(70.0 m - u * 7.00 s) / (7.00 s)^2
Now we can substitute the expression for u from part (a) into the equation for a, and solve for both u and a.
(a) Vav *t = [(V2 + V1)/2]*7 = 70
V2 = 15
V2/2 = 7.5 = 10 - (V1/2)
V1/2 = 2.5
V1 = 5 m/s
a = (V2 - V1)/t = 10/7.00 m/s^2