A bike rider accelerates constantly to a velocity of 7.4 m/s during 4.6 s. the bike's displacement is +18 m. What was the initial velocity of the bike?
To find the initial velocity of the bike, we can use the equation of motion:
v = u + at
Where:
v = final velocity = 7.4 m/s
u = initial velocity (what we are trying to find)
a = acceleration (constant during the given time)
t = time = 4.6 s
We are given that the displacement of the bike is +18 m. Displacement is given by the equation:
s = ut + (1/2)at^2
Since acceleration is constant, we can rearrange the equation as:
s = ut + (1/2)at^2
18 = u(4.6) + (1/2)a(4.6)^2
Now we have two equations with two unknowns (u and a). We need to solve these equations simultaneously.
Let's solve the second equation for a:
a = 2(18 - u(4.6))/(4.6)^2
Now substitute this value of a into the first equation:
v = u + at
7.4 = u + (2(18 - u(4.6))/(4.6)^2)(4.6)
Simplify the equation:
7.4 = u + (2(18 - 4.6u))/(4.6)
Multiply both sides by 4.6:
7.4(4.6) = 4.6u + 2(18 - 4.6u)
Simplify further:
33.94 = 4.6u + 36 - 9.2u
Combine like terms:
33.94 - 36 = -4.6u - 9.2u
-2.06 = -13.8u
Now isolate u:
-2.06 = -13.8u
u = -2.06 / -13.8
u ≈ 0.149 m/s
Therefore, the initial velocity of the bike was approximately 0.149 m/s.
To find the initial velocity of the bike, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
We have the final velocity (v = 7.4 m/s), the acceleration is constant, and the time is given as 4.6 s.
Since the displacement is not needed for this calculation, we can ignore it.
Now, let's rearrange the equation to solve for the initial velocity (u):
u = v - at
Substituting the given values:
u = 7.4 m/s - (a)(4.6 s)
Since we don't have the value of acceleration (a), we can't calculate the exact initial velocity. If you have the value of acceleration, you can substitute it into the equation to find the initial velocity.