Question

A cheetah, the fastest of all land animals over a short distance, accelerates from rest to $26m/s$. Assuming that the speed is constant, find the average speed of the cheetah:
\[\begin{align}
  & A.13m/s \\
 & B.9m/s \\
 & C.11m/s \\
 & D.10m/s \\
\end{align}\]

Answer 1

Hint: Speed is a scalar quantity which has only magnitude and not direction. We know that a speed is the change in the distance with respect to time. Clearly, speed depends on time. Then we can classify speed into average speed and instantaneous speed based on time.
Formula used:
$speed=\dfrac{distance}{time}$

Complete answer:
We know that speed is the change of distance with respect to time, and is given by $speed=\dfrac{distance}{time}$
Average speed is the change in distance $d$ over a period of time $t$, and is given as
 $u_{avg}=\dfrac{d}{t}$
Whereas, instantaneous speed is the small distance \[ds\] covered during a small period of time \[dt\]. It is denoted using calculus and is given as $u_{inst}=\dfrac{ds}{dt}$
Given that, acceleration of the cheetah from rest then, we can say that $a=26m/s$ and $u=0$ .
Clearly, to calculate average speed, we need to calculate the distance covered by the cheetah.
Let the time taken for which the average velocity is maintained to be $t=1s$
From the second law of motion we can calculate the distance covered during time $t$ by $s=ut+\dfrac{1}{2}at^{2}$.
Then we get $s=0\times 1+\dfrac{1}{2}\times 26\times 1^{2}=13m$
Then the average speed is, $speed_{avg}=\dfrac{13}{1}=13m/s$

So, the correct answer is “Option A”.

Additional Information:
We know that the acceleration is a vector quantity which has both direction and magnitude. It is the change in velocity of a body with respect to the time. A body undergoes acceleration when an external force is applied on the body.

Note:
The magnitude of can be both positive and negative. Negative acceleration is also known as deceleration. Since acceleration is dependent on the direction of motion, it can further be classified into linear and radial speed. But speed is only positive.