The time t when the velocity is 0 is t = a/2b.
The velocity of the projectile at time t = 4.
The velocity of the projectile at time t = 5.
Finding t for v = 0:
Define velocity:
The velocity of the projectile is represented by v and can be found using the derivative of the distance function:
v(t) = ds/dt = 4a - 8bt
Set velocity to zero:
We need to find the time t when the velocity is 0, so set v(t) equal to zero:
0 = 4a - 8bt
Solve for t:
Move the constant term to the right side:
4a = 8bt
Divide both sides by 8b:
t = a/2b
Therefore, the time t when the velocity is 0 is t = a/2b.
Finding v for t = 4:
Substitute t with 4:
Since we are asked for the velocity when t is 4, we need to substitute t = 4 in the velocity function:
v(4) = 4a - 8b(4)
Simplify the expression:
v(4) = 4a - 32b
This expression provides the velocity of the projectile at time t = 4.
Finding v for t = 5:
Substitute t with 5:
Similar to finding v for t = 4, substitute t = 5 in the velocity function:
v(5) = 4a - 8b(5)
Simplify the expression:
v(5) = 4a - 40b
This expression provides the velocity of the projectile at time t = 5.
Question
The distance s (in m) above the ground for a projectile firedvertically upward with a velocity of 4[a] * m / s as a function of timet(ins) is given s = 4 [a] * t - 4 [b] * t ^ 2
Your instructor will provide you with a and b.
Find the answers to these questions.
find t for v = 0
find v for t = 4
find v for t = 5