Question

Why is the answer B for this question? I know acceleration should be negative down but I don't know the other two variables.

Answer 1

B

Step-by-step explanation:

Displacement, velocity, and acceleration are vectors: they have magnitude and direction.

The convention is that "down" is negative and "up" is positive.

Thus, if an object is higher than when it started, its displacement is positive. If it is lower, the displacement is negative.

If it is still going "up", its velocity is positive. If it is falling, its velocity is negative.

1. Displacement

The formula for vertical displacement is

Δy = v₀t - ½gt²

If v₀ = 30 m/s, t = 2 s, and g = 9.8 m·s⁻², then

`\begin{array}{rcl}\Delta y & = & 30 *2 - (1)/(2)* 9.8 *2^(2)\\& = & 60 - 4.9 * 4\\& = & 60 - 19.6\\& = & \mathbf{40.4}\\\end{array}\\\text{The displacement is}\textbf{ up}}`

2. Velocity

The formula for vertical velocity is

v = v₀ - gt

If v₀ = 30 m/s, t = 2 s, and g = 9.8 m·s⁻², then

`\begin{array}{rcl}v & = & 30 - 9.8 * 2\\& = & 30 - 19.6\\& = & \mathbf{10.4}\\\end{array}\\\text{The velocity is}\textbf{ up}}`

3. Acceleration

The vertical acceleration is always -g = -9.8 m·s⁻².

The direction of the acceleration is down.

The only option with the sequence "up, up, down" is B.