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# A cheetah can accelerate at up to $6.0m/s^2$. How long does it take for a cheetah to speed up from $10.5m/s$ to $12.2m/s$?

Last updated date: 13th Jun 2024
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Hint: We know that acceleration is the rate of change of velocity with respect to time. Here the acceleration and initial and final speed of the cheetah is given, using the formula of acceleration we can solve the question to find the required time.
Formula used:
$a=\dfrac{dv}{dt}$

We know that the acceleration is the rate of change of velocity with respect to time, it is mathematically given as, $a=\dfrac{dv}{dt}$, where $a$ is the acceleration due to the change in velocity $d\;v$ during time $d\;t$ . Also, acceleration is a vector quantity which has both direction and magnitude. From Newton’s laws of motion we know that a body undergoes acceleration when an external force is applied on the body and given as $F=ma$ where, $F$ is the force, $m$ is mass and $a$ is acceleration.
Here, it is given that the cheetah accelerates $a=6m/s^{2}$. The initial velocity is given as $u=10.5m/s$ and final velocity is given as $v=12.2m/s$
Then from the formula, we get,
$dt=\dfrac{a}{dv}$
$\implies dt=\dfrac{6}{12.2-10.5}$
$\implies dt=\dfrac{6}{1.7}$
$\implies dt=3.57 s$
Thus the total time taken for the acceleration is $3.57\;s$

Alternatively, we can solve the question using the equation of motion, from $v=u+at$. The other equations of motion are:
$s=ut+\dfrac{1}{2}at^{2}$
$v^{2}-u^{2}=2as$