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A car of mass 1200kg starting from 15m/s achieved the velocity of 66m/s ,If 6572N force is applied then find out time taken and acceleration.

Note:-

If p/q form arises find answer in decimals .


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Sagot :

Fieryanswererftidn

Answer:

acceleration: 5.48 m/s²

time taken: 9.3 seconds

Given:

  • mass: 1200 kg
  • force: 6572 N
  • initial velocity: 15 m/s
  • final velocity: 66 m/s

[tex]\boxed{\sf acceleration = \dfrac{Force}{mass}}[/tex]    [tex]\boxed{\sf time \ taken = \dfrac{final \ velocity - initial \ velocity}{acceleration} }[/tex]

using the formula's:

answer 1:

[tex]\sf acceleration = \dfrac{F}{m}[/tex]

[tex]\sf acceleration = \dfrac{6572 }{1200 }[/tex]

[tex]\sf acceleration = 5.4766... \ m/s^2[/tex]

[tex]\sf acceleration = 5.48 \ m/s^2[/tex]             // rounded to nearest hundredth //

answer 2:

[tex]\sf time \ taken = \dfrac{\Delta v}{a}[/tex]

[tex]\sf time \ taken = \dfrac{66 - 15}{5.48}[/tex]

[tex]\sf time \ taken = 9.3122 \ seconds[/tex]

[tex]\sf time \ taken = 9.3 \ seconds[/tex]           // rounded it to nearest tenth //

VirαtKσhliidn

Answer:

[tex]\large\boxed{\sf Time =9.30\ s }[/tex]

[tex]\large\boxed{\sf Accl^n =5.47\ m/s^2 }[/tex]

Explanation:

Here it is given that a car of mass 1200kg has an initial velocity of 15m/s achieves a velocity of 66m/s . A force of 6572N was applied in order to increase the velocity and we need to find the time taken in doing so .

From Newton's Second Law of Motion ,

  • The rate of change of momentum is directly proportional to the applied force in the direction of the force . Mathematically ,

[tex]\sf\qquad\longrightarrow Force = \triangle p\\\\ [/tex]

As momentum (p) = mass × velocity ,

[tex]\\\sf\qquad\longrightarrow Force = \dfrac{m(v-u)}{t} \\\\ [/tex]

Here ,

  • u = 15m/s
  • v = 66m/s
  • Force = 6572N

• On substituting the respective values ,

[tex]\sf\qquad\longrightarrow 6572N = \dfrac{1200kg ( 66- 15 )m/s }{t}\\\\ [/tex]

[tex]\sf\qquad\longrightarrow 6572N = 1200kg \times \dfrac{51}{t} \\\\ [/tex]

[tex]\sf\qquad\longrightarrow t = \dfrac{1200×51}{6572N } \\\\ [/tex]

[tex]\sf\qquad\longrightarrow t =\dfrac{61200}{6572}s \\\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{\frak{ Time = 9.30\ s }} [/tex]

• For finding acceleration ,

[tex]\sf\qquad\longrightarrow Force = mass * acceleration \\\\ [/tex]

[tex]\sf\qquad\longrightarrow accl^n =\dfrac{Force}{mass} \\\\ [/tex]

[tex]\sf\qquad\longrightarrow accl^n =\dfrac{6572N }{1200kg} \\\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{\frak{ acceleration= 5.47\ m/s^2}} \\\\ [/tex]

[tex]\rule{200}4[/tex]

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