Answer
384.9k+ views
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:
$a=\dfrac{dv}{dt}$
Complete answer:
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 $3.57\;s$
Additional information:
Alternatively, we can solve the question using the equation of motion, from $v=u+at$. The other equations of motion are:
$s=ut+\dfrac{1}{2}at^{2}$
$v^{2}-u^{2}=2as$
Note:
The magnitude of acceleration 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, which is due to motion in a straight line and radial speed, which is due to circular motion. But speed is only positive, as it’s a scalar quantity which has magnitude and no direction.
Formula used:
$a=\dfrac{dv}{dt}$
Complete answer:
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 $3.57\;s$
Additional information:
Alternatively, we can solve the question using the equation of motion, from $v=u+at$. The other equations of motion are:
$s=ut+\dfrac{1}{2}at^{2}$
$v^{2}-u^{2}=2as$
Note:
The magnitude of acceleration 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, which is due to motion in a straight line and radial speed, which is due to circular motion. But speed is only positive, as it’s a scalar quantity which has magnitude and no direction.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)