Question

instantaneous speed
the instantaneous speed of an object is its speed at a
given instant, or point in time. because we cannot divide
by zero, we cannot use the equation for speed to calcu-
late instantaneous speed. however, tools like the speed-
ometers in cars can measure instantaneous speed. if an
object is moving at a constant speed, its instantaneous
speed is equal to its constant speed.

how can you calculate velocity?
remember that velocity is the speed of an object in
a particular direction. to calculate the velocity of an
object, you must first find the speed of the object. then,
you must indicate the direction of the object. lets look at
an example.

for several days in 1936, alaskas black rapids gla-
cier moved at 89 m per day down the valley. what is the
velocity of the glacier in meters per second?

step 1: list the given and unknown values.	given: ( d = 89 , \text{m} ) ( t = 1 , \text{day} ) direction = down the valley	unknown: velocity, ( v )
step 3: insert the known values and solve for the unknown value.	( v = \frac{89 , \text{m}}{86,400 , \text{s}} ) ( v = 0.0010 , \text{m/s} ) down the valley

so, the glacier moved at a velocity of 0.0010 m/s down
the valley. notice that the symbol for velocity, ( v ), is the
same as the symbol for speed. you can use the speed
equation to calculate velocity. just remember to include a
direction when you describe an object’s velocity.

how can you show motion on a graph?
you can show motion on a graph by recording distance
on the vertical axis and time on the horizontal axis. then,
you can use the shape of the line on the graph to learn
about the motion of an object.

reading check

1. explain why can’t you

use the speed equation
to calculate instantaneous
speed?

math skills

1. calculate a swimmer

swims 110 m toward the
shore in 72 s. what is the
swimmer’s velocity in meters
per second? show your work.

Explanation:

For Question 9 (Reading Check)

To calculate instantaneous speed, we need the speed at a specific instant (time approaches zero). The speed equation is \( v=\frac{d}{t} \), and dividing by zero (as \( t \) approaches 0 for an instant) is mathematically undefined, so we can't use the speed equation for instantaneous speed.

Step1: Identify given and unknown values

Given: Distance \( d = 110\space m \), Time \( t = 72\space s \), Direction = toward the shore. Unknown: Velocity \( v \). The formula for velocity (since velocity is speed with direction, and speed is \( \frac{d}{t} \)) is \( v=\frac{d}{t} \).

Step2: Substitute values into the formula

Substitute \( d = 110\space m \) and \( t = 72\space s \) into \( v=\frac{d}{t} \). So, \( v=\frac{110}{72}\space m/s \).

Step3: Calculate the value

Simplify \( \frac{110}{72}\approx1.53\space m/s \). Then, include the direction (toward the shore) for velocity.

Answer:

We can't use the speed equation (\( v = \frac{d}{t} \)) to calculate instantaneous speed because instantaneous speed is at a given instant (time \( t \) approaches 0), and dividing by zero is mathematically undefined.

For Question 10 (Math Skills)