Question

Examine the scenario.

A car starts from rest and uniformly accelerates to a speed of 40 km/h in 5 s. The car moves south the entire time.

Which option correctly lists a vector quantity from the scenario?

distance: 40 km
velocity: 5 km/h north
acceleration 8 km/h/s south
speed: 40 km/h

Answer 1

acceleration 8 km/h/s south

Step-by-step explanation:

First of all, let's remind that a vector quantity is a quantity which has both a magnitude and a direction.

Based on this definition, we can already rule out the following two choices:

distance: 40 km

speed: 40 km/h

Since they only have magnitude, they are not vectors.

Then, the following option:

velocity: 5 km/h north

is wrong, because the car is moving south, not north.

So, the correct choice is

acceleration 8 km/h/s south

In fact, the acceleration can be calculated as

`a=(v-u)/(t)`

where

v = 40 km/h is the final velocity

u = 0 is the initial velocity

t = 5 s is the time

Substituting,

`a=(40 km/h-0)/(5 s)=8 km/h/s`

And since the sign is positive, the direction is the same as the velocity (south).