Question

the displacement x=3-5t+2t*t find its velocity at t=2sec. and acceleration at t=4sec. in process
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Answer 1

Given:-

• Displacement of a body, x = 3 - 5t + 2t² where t is time.

To find:-

• Velocity of body at t = 2 sec
• Acceleration of body at t = 4 sec

Formulae required:-

• Formula for the instantaneous velocity at an instant 't'

        v(t) = d(x) / d(t)

• Formula for the instantaneous acceleration at an instant 't'

        a(t) = d(v) / d(t)

[Where 'v' is velocity, 'x' is displacement, 't' is time and 'a' is acceleration]

Solution:-

Calculating the instantaneous velocity of body at an instant 't'

→ v(t) = d(x) / d(t)

→ v(t) = d(2t² - 5t + 3) / d(t)

→ v(t) = 4t - 5 m/s

So, velocity of body at t=2 s

→ v(2) = 4(2) - 5 = 8 - 5

→ v(2) = 3 m/s

Now, calculating the instantaneous acceleration of body at an instant 't'

→ a(t) = d(v) / d(t)

→ a(t) = d(4t - 5) / d(t)

→ a(t) = 4 m/s²

Here we got that acceleration of body is a constant for any instant of time.

Hence,

• Velocity of body at t=2 sec is 3 m/s. and
• Acceleration of body at t=4 sec is 4 m/s².

Answer 2

Given:-

$\longrightarrow$Displacement = $\bold{x = 3 - 5t + 2t \times 2.}$

To Prove:-

$\longrightarrow$Velocity and Acceleration

Solution:-

$\longrightarrow$Using Formula,

${ \boxed{ \boxed{ \boxed{ \bold{ \orange{v = \frac{d \times x}{d \times t} }}}}}}$

$\bold{0 - 5 + 22 \times t}$

$\bold{4t - 5}$

$\longrightarrow$Now, velocity at 2 seconds :

$\bold{4 \times 2 - 5}$

$\bold{8 - 5}$

$\bold{3 m/s}$

$\longrightarrow$Hence, Instantaneous velocity at time of 2 seconds $\bold{= 3 m/s.}$

$\longrightarrow$Now, Instantaneous acceleration : 4 - 0 = $\bold{4 m/s}$