First slide

Instantaneous velocity

Question

The displacement of a particle is given by $y = a + bt + {ct}^{2} - {dt}^{4}$ . The initial velocity is

Moderate

A

a
B

c
C

b
D

-d

Solution

$\begin{array}{l} y = a + bt + {ct}^{2} - {dt}^{4} \\ ∴ v = \frac{dy}{dt} = b + 2 ct - 4 {dt}^{3} \end{array}$
Hence, at t = 0, v_initial = b

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