Question

How do I find initial velocity and time?

I am given final velocity which is 10, acceleration which is 20, and displacement which is -100. I keep getting 64.031 but my teacher says that initial velocity can’t be greater than final velocity if the acceleration is positive which makes sense, but I don’t know how to get another answer. Help?

Answer 1

Step-by-step explanation:

Given:

Δx = -100

v = 10

a = 20

To find v₀, use a kinematic equation that's independent of time.

v² = v₀² + 2aΔx

(10)² = v₀² + 2(20)(-100)

100 = v₀² − 4000

v₀² = 4100

v₀ = ±64.0

As your teacher said, v₀ can't be +64.0. So v₀ = -64.0.

Next, to find time, use a kinematic equation that's independent of initial velocity.

Δx = vt − ½ at²

-100 = (10) t − ½ (20) t²

-100 = 10 t − 10 t²

-10 = t − t²

t² − t − 10 = 0

Solve with quadratic formula:

t = [ -(-1) ± √((-1)² − 4(1)(-10)) ] / 2(1)

t = (1 ± √41) / 2

t > 0, so:

t = (1 + √41) / 2

t ≈ 3.70