Question

The displacement x of an object is given as a function of time,x=2t+3t square. Calculate the instantaneous velocity of the object at t = 2s

Answer 1

x = 2t+3t²

We know, Differentiation of displacement gives instantaneous velocity.

v = dx/dt = d2t+3t²/dt

=> d2t/dt + d3t²/dt

=> 2t¹-¹ + 3×2t²-¹

=>2 + 6t

Instantaneous speed at t = 2s is 2+6×2 =>2+12 => 14m/s

Cheers!

Answer 2

Answer:

Instantaneous velocity of the object at time t = 2s is 14 m/s.

Explanation:

It is given that -

• Displacement x of an object is given as a function of time : $\sf{\red{x = 2t + 3t^2}}$

We've to find the instantaneous velocity at time 2s.

Solution:

x = 2t + 3t²

$\longrightarrow$ v = $\dfrac{dx}{dt}$

$\longrightarrow$ v = 2 + 6t

Substitute the value of t as 2,

$\longrightarrow$ v = 2 + 6 (2)

$\longrightarrow$ v = 2 + 12

$\longrightarrow$ v = 14 m/s

Hence, instantaneous velocity of the object as time 2s is 14 m/s.