Question

A body starts from rest with uniform acceleration band travels 360m in 4s. Find the velocity after 15s and total distance travelled.​

Answer 1

PART 1 :

As per the given data

• initial velocity= 0 m/s

• distance traveled = 360 m

• time taken = 4 s

We need to figure nd the acceleration of the body by using the given data

As the body moves with uniform acceleration let's use the second equation of motion in order to solve this part

$\bigstar \boxed{ \mathtt{s = ut + \dfrac{1}{2} a {t}^{2} }}$

here ,

• s = distance travelled
• u = initial velocity
• t = time taken
• a = acceleration

$\rightarrow \mathtt{s = \dfrac{1}{2} a {t}^{2} }$

$\rightarrow \mathtt{a = \dfrac{2s}{ {t}^{2} } }$

substituting the given values in the above equation we get,

$\rightarrow \mathtt{a = \dfrac{ \cancel2 \times 360}{ \cancel{16}} }$

$\rightarrow \mathtt{a = \dfrac{360}{8} }$

$\rightarrow \mathtt{ \pink{a = 45 \dfrac{m}{ {s}^{2} } }}$

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PART II :

As per the given data ,

• Initial velocity = 0 m/s
• acceleration = 45 m / s²
• time taken = 15 s

As the body moves with uniform acceleration let's use the second kinematics equation in order to get the distance

$\bigstar \boxed{ \mathtt{s = ut + \dfrac{1}{2} a {t}^{2} }}$

substituting the given values in the above equation we get,

$\rightarrow \mathtt{s \: = \dfrac{1}{2} a {t}^{2} }$

$\rightarrow \mathtt{s \: = \dfrac{1}{2} \times 45 \times 15 \times 15}$

$\rightarrow \mathtt{s \: = \dfrac{45 \times 225}{2} }$

$\rightarrow \mathtt{s \: = \dfrac{10125}{2} }$

$\rightarrow \mathtt{ \red{s \: = 5062.5 \: m}}$

The total distance travelled by the body after 15 seconds is 5062.5 m

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Now in order to find the final velocity of the body let's use the first kinematics equation,

$\bigstar \large\boxed{ \mathtt{v = u + at}}$

here ,

• v= final velocity
• u = initial velocity
• a= acceleration
• t = time taken

substituting the given values in the above equation we get,

$\rightarrow \mathtt{v = at}$

$\rightarrow \mathtt{v = 45 \times 15}$

$\rightarrow \mathtt{ \orange{v = 675 \dfrac{m}{s} }}$

The final velocity of the body after 15 seconds 675 m/s