Question

the velocity of a car doubles over a short period of time. which additional information is sufficient to determine the amount of acceleration during this time period?

• the car’s initial velocity and the final velocity
• the car’s initial velocity and the time period
• the car’s initial direction of motion and the final direction of motion
• the car’s rate of motion and the direction of motion

Explanation:

Acceleration is defined as $\frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}$, where $v_f$ is final velocity, $v_i$ is initial velocity, and $t$ is time. The problem states $v_f = 2v_i$.

• Option 1: We already know $v_f = 2v_i$, so this gives no new info to find $t$.
• Option 2: With $v_i$ and $t$, we can calculate $v_f=2v_i$, then use $a=\frac{2v_i - v_i}{t}=\frac{v_i}{t}$ to find acceleration.
• Option 3: Direction does not affect the magnitude of acceleration here.
• Option 4: Rate of motion (speed) without time, and direction, does not allow calculation of acceleration.

Answer:

the car's initial velocity and the time period