First slide

Instantaneous acceleration

Question

The displacement of a particle moving along x-axis is given by :
$x = a + bt + {ct}^{2}$
The acceleration of the particle is

Easy

A

b
B

c
C

b+c
D

2c

Solution

$x = a + bt + {ct}^{2}$
velocity v = $\frac{dx}{dt} = 0 + b + c . 2 t = b + 2 ct$
acceleration f = $\frac{dv}{dt} = 0 + 2 c = 2 c$

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