Question

3. A cheetah is known to be the fastest mammal on Earth, at least for short
runs. Cheetahs have been observed running a distance of 5.50 x 102 m
with an average speed of 1.00 x 10 km/h.
a. How long would it take a cheetah to cover this distance at this speed?
b. Suppose the average speed of the cheetah were just 85.0 km/h.
What distance would the cheetah cover during the same time inter-
val calculated in (a)?​

Answer 1

Answers:

a) 198,55 s

b) 4687.98 m

Explanation:

a) Speed $v$ is defined as the variation of the position (distance traveled $d$)of a body or object with time $t$:

$v=\frac{d}{t}$ (1)

We are told the cheetah runs a distance of  $d=5.50(10)^{2}m=550m$ with a speed $v=10\frac{km}{h}=2.77\frac{m}{s}$ (Knowing $1km=1000m$ and $1h=3600s$), and we need to find the time it takes to travel that distance.

This means we have to find $t$ from (1):

$t=\frac{d}{v}$ (2)

$t=\frac{550m}{2.77\frac{m}{s}}$ (3)

$t=198.55s$ (4)

b) Now, if we want to know the distance the cheetah will cover with $v=85\frac{km}{h}=23.61\frac{m}{s}$ in $t=198.55s$, we have to isolate $d$ from (1):

$d=v.t$ (5)

$d=(23.61\frac{m}{s})(198.55s)$ (6)

Finally:

$d=4687.98m$

Answer 2

The time taken for the cheetah to cover the distance of 5.50×10² m and the distance covered by the cheetah during the same time interval at an average speed of 85.0 km/h are:

1. The time taken for the cheetah to cover the distance of 5.50×10² m is 197.8 s.

2. The distance covered by the cheetah during the same time interval at an average speed of 85.0 km/h is 4670.06 m.

Average speed is obtained by dividing the total distance by the total time taken to cover the distance.

$Average speed = \frac{Total distance}{total time}$

1. Determination of the time taken for cheetah to cover the distance of 5.50×10² m.

Average speed = 10 Km/h = 10 / 3.6 = 2.78 m/s

Distance = 5.50×10²

Time =?

$Time = \frac{Distance}{average speed } \\\\Time = \frac{5.50*10^{2}}{2.78}$

Time = 197.8 s

Thus, the time taken for cheetah to cover the distance of 5.50×10² m is 197.8 s

2. Determination of the distance covered by the cheetah during the same time interval.

Time = 197.8 s

Average speed = 85 Km/h = 85 / 3.6 = 23.61 m/s

Distance =?

Distance = Average speed × Time

Distance = 23.61 × 197.8

Distance = 4670.06 m

Thus, the distance covered by the cheetah during the same time interval is 4670.06 m

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