Question

Given that v = 2 + 5t (in SI units), using this equation, find its acceleration.​

Answer 1

SOLUTION

GIVEN

v = 2 + 5t (in SI units),

TO DETERMINE

The acceleration using this equation

EVALUATION

Here it is given that

v = 2 + 5t

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{dv}{dt} = \frac{d}{dt} (2 + 5t) }$

$\displaystyle \sf{ \implies \frac{dv}{dt} = \frac{d}{dt} (2) + \frac{d}{dt} (5t) }$

$\displaystyle \sf{ \implies \frac{dv}{dt} = 0+5 \frac{d}{dt} (t) }$

$\displaystyle \sf{ \implies \frac{dv}{dt} = 5}$

FINAL ANSWER

Acceleration = 5 m/s²

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Answer 2

Given : v = 2 + 5t (In SI units),

To Find :  acceleration​

2 m/s²

3 m/s²

4 m/s²

5 m/s²

Solution:

v = 2 + 5t (In SI units),

v  - velocity unit  m/s

t   time unit  secs

a  acceleration unit  = m/s²

acceleration is rate of change of velocity

a = dv/dt

v = 2 + 5t

a  =(d/dt)( 2 + 5t)

=> a = (d/dt)(2)  + (d/dt)(5t)

=> a = 0   + 5

=> a = 5

acceleration​ is 5 m/s²

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