Question

The motion of the car is provided by the function x = 4t2 + 10t + 6. Compute its Instantaneous Velocity at time t = 5s.​

Answer 1

Solution :-

Given: The function is x = 4t² + 10t + 6.

Differentiating the provided function with respect to t, we get

$\tt \implies \: { \rm{ \boxed{\red{ \rm{ \underline{V_{inst} \: = \frac{dx}{dt} }}}} }}$

$\tt \implies \: { \rm{ { {V_{inst} \: = \frac{d(4t {}^{2} + 10t + 6) }{dt} }}}}$

For time t = 5s, the Instantaneous Velocity is articulated as,

$\implies$ V(t) = 8t + 10

$\implies$ V(5) = 8(5) + 10

$\implies$ V(5)= 50 m/s.

Thus for the known function, Instantaneous Velocity is 50 m/s.